Mathematical Physics

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aria-labelledby="recent-math-ph" href="/list/math-ph/recent">recent</a> articles</p> <h3>Showing new listings for Friday, 22 November 2024</h3> <div class='paging'>Total of 45 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math-ph/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> <dl id='articles'> <h3>New submissions (showing 9 of 9 entries)</h3> <dt> <a name='item1'>[1]</a> <a href ="/abs/2411.13857" title="Abstract" id="2411.13857"> arXiv:2411.13857 </a> [<a href="/pdf/2411.13857" title="Download PDF" id="pdf-2411.13857" aria-labelledby="pdf-2411.13857">pdf</a>, <a href="https://arxiv.org/html/2411.13857v1" title="View HTML" id="html-2411.13857" aria-labelledby="html-2411.13857" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13857" title="Other formats" id="oth-2411.13857" aria-labelledby="oth-2411.13857">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Ivanov,+A+V">A. V. Ivanov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> LaTeX, 30 pages, 1 figure. Firstly appeared in Russian, November 15, 2024, see <a href="https://www.pdmi.ras.ru/preprint/2024/24-11.html" rel="external noopener nofollow" class="link-external link-https">this https URL</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; High Energy Physics - Theory (hep-th) </div> <p class='mathjax'> The paper studies a regularization of the quantum (effective) action for a scalar field theory in a general position on a compact smooth Riemannian manifold. As the main method, we propose the use of a special averaging operator, which leads to a quasi-locality and is a natural generalization of a cutoff regularization in the coordinate representation in the case of a curved metric. It is proved that the regularization method is consistent with a process of gluing of manifolds and partition functions, that is, with the transition from submanifolds to the main manifold using an additional functional integration. It is shown that the method extends to other models, and is also consistent with the process of multiplicative renormalization. Additionally, we discuss issues related to the correct introduction of regularization and the locality. </p> </div> </dd> <dt> <a name='item2'>[2]</a> <a href ="/abs/2411.13864" title="Abstract" id="2411.13864"> arXiv:2411.13864 </a> [<a href="/pdf/2411.13864" title="Download PDF" id="pdf-2411.13864" aria-labelledby="pdf-2411.13864">pdf</a>, <a href="https://arxiv.org/html/2411.13864v1" title="View HTML" id="html-2411.13864" aria-labelledby="html-2411.13864" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13864" title="Other formats" id="oth-2411.13864" aria-labelledby="oth-2411.13864">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Einstein metrics on homogeneous superspaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Zhang,+Y">Yang Zhang</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Gould,+M+D">Mark D. Gould</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Pulemotov,+A">Artem Pulemotov</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Rasmussen,+J">Jorgen Rasmussen</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 46 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; High Energy Physics - Theory (hep-th); Differential Geometry (math.DG) </div> <p class='mathjax'> This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous supermanifolds by means of Dynkin diagrams, resembling the construction of generalised flag manifolds in classical (non-super) theory. We describe the Einstein metrics on several classes of spaces obtained through this approach. Our results provide examples of compact homogeneous supermanifolds on which the Einstein equation has no solutions, discrete families of solutions, and continuous families of Ricci-flat solutions among invariant metrics. These examples demonstrate that the finiteness conjecture from classical homogeneous geometry fails on supermanifolds, and challenge the intuition furnished by Bochner's vanishing theorem. </p> </div> </dd> <dt> <a name='item3'>[3]</a> <a href ="/abs/2411.13977" title="Abstract" id="2411.13977"> arXiv:2411.13977 </a> [<a href="/pdf/2411.13977" title="Download PDF" id="pdf-2411.13977" aria-labelledby="pdf-2411.13977">pdf</a>, <a href="https://arxiv.org/html/2411.13977v1" title="View HTML" id="html-2411.13977" aria-labelledby="html-2411.13977" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13977" title="Other formats" id="oth-2411.13977" aria-labelledby="oth-2411.13977">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Long-range effects in asymptotic fields and angular momentum of classical field electrodynamics </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Herdegen,+A">Andrzej Herdegen</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 44 pages; this is an old article (1995) which may be of interest in connection with more recent works (in particular, <a href="https://arxiv.org/abs/2403.09234" data-arxiv-id="2403.09234" class="link-https">arXiv:2403.09234</a>) </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> J. Math. Phys. 36 (1995) 4044-4086 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; High Energy Physics - Theory (hep-th) </div> <p class='mathjax'> Asymptotic properties of classical field electrodynamics are considered. Special attention is paid to the long-range structure of the electromagnetic field. It is shown that conserved Poincare quantities may be expressed in terms of the asymptotic fields. Long-range variables are shown to be responsible for an angular momentum contribution which mixes Coulomb and infrared free field characteristics; otherwise angular momentum and energy-momentum separate into electromagnetic and matter fields contributions. </p> </div> </dd> <dt> <a name='item4'>[4]</a> <a href ="/abs/2411.14015" title="Abstract" id="2411.14015"> arXiv:2411.14015 </a> [<a href="/pdf/2411.14015" title="Download PDF" id="pdf-2411.14015" aria-labelledby="pdf-2411.14015">pdf</a>, <a href="https://arxiv.org/html/2411.14015v1" title="View HTML" id="html-2411.14015" aria-labelledby="html-2411.14015" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14015" title="Other formats" id="oth-2411.14015" aria-labelledby="oth-2411.14015">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the geometry of isomonodromic deformations on the torus and the elliptic Calogero-Moser system </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Alameddine,+M">Mohamad Alameddine</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 25 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; Symplectic Geometry (math.SG); Exactly Solvable and Integrable Systems (nlin.SI) </div> <p class='mathjax'> We consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlev茅 equation. We establish an extended symmetry, complementing known results. The Calogero-Moser system in its elliptic version is shown to fit nicely in the geometric framework, the extended symplectic two-form is introduced and shown to be closed. </p> </div> </dd> <dt> <a name='item5'>[5]</a> <a href ="/abs/2411.14028" title="Abstract" id="2411.14028"> arXiv:2411.14028 </a> [<a href="/pdf/2411.14028" title="Download PDF" id="pdf-2411.14028" aria-labelledby="pdf-2411.14028">pdf</a>, <a href="https://arxiv.org/html/2411.14028v1" title="View HTML" id="html-2411.14028" aria-labelledby="html-2411.14028" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14028" title="Other formats" id="oth-2411.14028" aria-labelledby="oth-2411.14028">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Global well-posedness in a Hartree-Fock model for graphene </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Borrelli,+W">William Borrelli</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Morellini,+U">Umberto Morellini</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 21 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Analysis of PDEs (math.AP) </div> <p class='mathjax'> Graphene is a monolayer graphitic film where electrons behave like two-dimensional Dirac fermions without mass. Its study has attracted a wide interest in the domain of condensed matter physics. In particular, it represents an ideal system to test the comprehension of 2D massless relativistic particles in a laboratory, the Fermi velocity being $300$ times smaller than the speed of light. In this work, we present a global well-posedness result for graphene in the Hartree-Fock approximation. The model allows to describe the time evolution of graphene in the presence of external electric fields, such as those induced by local defects in the monolayer of carbon atoms. Our approach is based on a well established non-perturbative framework originating from the study of three-dimensional quantum electrodynamics. </p> </div> </dd> <dt> <a name='item6'>[6]</a> <a href ="/abs/2411.14139" title="Abstract" id="2411.14139"> arXiv:2411.14139 </a> [<a href="/pdf/2411.14139" title="Download PDF" id="pdf-2411.14139" aria-labelledby="pdf-2411.14139">pdf</a>, <a href="https://arxiv.org/html/2411.14139v1" title="View HTML" id="html-2411.14139" aria-labelledby="html-2411.14139" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14139" title="Other formats" id="oth-2411.14139" aria-labelledby="oth-2411.14139">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the Classification of the L\'evy-Leblond Spinors </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Miranda,+L">Luiza Miranda</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=de+Freitas,+I+P">Isaque P. de Freitas</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Toppan,+F">Francesco Toppan</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 8 pages; based on the L. M.'s talk at ISQS28, Prague, July 1-5, 2024; to appear in the Proceedings </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph) </div> <p class='mathjax'> The first-order L茅vy-Leblond differential equations (LLEs) are the non-relativistic analogous of the Dirac equation: they are the "square roots" of the Schr枚dinger equation in ($1+d$) dimensions and admit spinor solutions. In this paper we show how to extend to the L茅vy-Leblond spinors the real/complex/quaternionic classification of the relativistic spinors (which leads to the notions of Dirac, Weyl, Majorana, Majorana-Weyl, Quaternionic spinors). Besides the free equations, we also consider the presence of potential terms. Applied to a conformal potential, the simplest $(1+1)$-dimensional LLE induces a new differential realization of the $osp(1|2)$ superalgebra in terms of differential operators depending on the time and space coordinates. </p> </div> </dd> <dt> <a name='item7'>[7]</a> <a href ="/abs/2411.14171" title="Abstract" id="2411.14171"> arXiv:2411.14171 </a> [<a href="/pdf/2411.14171" title="Download PDF" id="pdf-2411.14171" aria-labelledby="pdf-2411.14171">pdf</a>, <a href="/format/2411.14171" title="Other formats" id="oth-2411.14171" aria-labelledby="oth-2411.14171">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A rigorous Peierls-Onsager effective dynamics for semimetals in long-range magnetic fields </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Cornean,+H+D">Horia D. Cornean</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Helffer,+B">Bernard Helffer</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Purice,+R">Radu Purice</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 59 pages, 2 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span> </div> <p class='mathjax'> We consider periodic (pseudo)differential {elliptic operators of Schr枚dinger type} perturbed by weak magnetic fields not vanishing at infinity, and extend our previous analysis in \cite{CIP,CHP-2,CHP-4} to the case {of a semimetal having a finite family of Bloch eigenvalues whose range may overlap with the other Bloch bands but remains isolated at each fixed quasi-momentum.} We do not make any assumption of triviality for the associated Bloch bundle. In this setting, we formulate a general form of the Peierls-Onsager substitution {via strongly localized tight-frames and magnetic matrices. We also} prove the existence of an approximate time evolution for initial states supported inside the range of the isolated Bloch family, with a precise error control. </p> </div> </dd> <dt> <a name='item8'>[8]</a> <a href ="/abs/2411.14178" title="Abstract" id="2411.14178"> arXiv:2411.14178 </a> [<a href="/pdf/2411.14178" title="Download PDF" id="pdf-2411.14178" aria-labelledby="pdf-2411.14178">pdf</a>, <a href="https://arxiv.org/html/2411.14178v1" title="View HTML" id="html-2411.14178" aria-labelledby="html-2411.14178" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14178" title="Other formats" id="oth-2411.14178" aria-labelledby="oth-2411.14178">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Mathematical aspects of space-time horizontal ray method </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Kaplun,+A">Aleksandr Kaplun</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Katsnelson,+B">Boris Katsnelson</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span> </div> <p class='mathjax'> The following development of the well-known "vertical modes and horizontal rays" approach for acoustic waves propagation in shallow water, introduced in different works, is studied. In this approach we study so-called space-time horizontal rays, constructed on the base of decomposition of the sound field, depending on time, over adiabatic vertical modes (solutions of the Sturm-Liouville problem). Using this technique we obtain different properties of signals, propagating in underwater waveguide, such as space-time caustics, and provide rather simple method for the prediction of the form of the signal and all its parameters (amplitude and frequency modulation, different front angles, etc.) at some point of observation. </p> </div> </dd> <dt> <a name='item9'>[9]</a> <a href ="/abs/2411.14391" title="Abstract" id="2411.14391"> arXiv:2411.14391 </a> [<a href="/pdf/2411.14391" title="Download PDF" id="pdf-2411.14391" aria-labelledby="pdf-2411.14391">pdf</a>, <a href="https://arxiv.org/html/2411.14391v1" title="View HTML" id="html-2411.14391" aria-labelledby="html-2411.14391" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14391" title="Other formats" id="oth-2411.14391" aria-labelledby="oth-2411.14391">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Phase Space Representation of the Density Operator: Bopp Pseudodifferential Calculus and Moyal Product </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=de+Gosson,+M">Maurice de Gosson</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; Operator Algebras (math.OA); Quantum Physics (quant-ph) </div> <p class='mathjax'> Bopp shifts were introduced in 1956 in the study of statistical interpretations of quantum mechanics. They lead to a phase space view of quantum mechanics closely related to the Moyal star product and its interpretation as a deformation quantization. In the present paper we pursue our study of Bopp quantization by initiated in previous work and apply it to give a new phase space description of the density operator, that is of the mixed states of quantum mechanics. </p> </div> </dd> </dl> <dl id='articles'> <h3>Cross submissions (showing 19 of 19 entries)</h3> <dt> <a name='item10'>[10]</a> <a href ="/abs/2411.12190" title="Abstract" id="2411.12190"> arXiv:2411.12190 </a> (cross-list from cond-mat.mes-hall) [<a href="/pdf/2411.12190" title="Download PDF" id="pdf-2411.12190" aria-labelledby="pdf-2411.12190">pdf</a>, <a href="https://arxiv.org/html/2411.12190v1" title="View HTML" id="html-2411.12190" aria-labelledby="html-2411.12190" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.12190" title="Other formats" id="oth-2411.12190" aria-labelledby="oth-2411.12190">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Higher-dimensional magnetic Skyrmions </div> <div class='list-authors'><a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Gudnason,+S+B">Sven Bjarke Gudnason</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Bolognesi,+S">Stefano Bolognesi</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Menta,+R">Roberto Menta</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> LaTeX: 40 pages, 14 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mesoscale and Nanoscale Physics (cond-mat.mes-hall)</span>; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) </div> <p class='mathjax'> We propose a generalization of the theory of magnetic Skyrmions in chiral magnets in two dimensions to a higher-dimensional theory with magnetic Skyrmions in three dimensions and an $S^3$ target space, requiring a 4-dimensional magnetization vector. A physical realization of our theory necessitates the use of a synthetic dimension, recently promoted and realized in condensed matter physics. In the simplest incarnation of the theory, we find a Skyrmion and a sphaleron - the latter being an unstable soliton. Including also the Skyrme term in theory enriches the spectrum to a small metastable Skyrmion, an unstable sphaleron and a large stable Skyrmion. </p> </div> </dd> <dt> <a name='item11'>[11]</a> <a href ="/abs/2411.13575" title="Abstract" id="2411.13575"> arXiv:2411.13575 </a> (cross-list from math.AP) [<a href="/pdf/2411.13575" title="Download PDF" id="pdf-2411.13575" aria-labelledby="pdf-2411.13575">pdf</a>, <a href="https://arxiv.org/html/2411.13575v1" title="View HTML" id="html-2411.13575" aria-labelledby="html-2411.13575" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13575" title="Other formats" id="oth-2411.13575" aria-labelledby="oth-2411.13575">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On reconstruction from imaginary part for radiation solutions in two dimensions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Nair,+A">Arjun Nair</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Novikov,+R">Roman Novikov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> arXiv admin note: substantial text overlap with <a href="https://arxiv.org/abs/2405.10333" data-arxiv-id="2405.10333" class="link-https">arXiv:2405.10333</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> We consider a radiation solution $\psi$ for the Helmholtz equation in an exterior region in $\mathbb R^2$. We show that $\psi$ in the exterior region is uniquely determined by its imaginary part $Im(\psi)$ on an interval of a line $L$ lying in the exterior region. This result has holographic prototype in the recent work [Nair, Novikov, <a href="https://arxiv.org/abs/2408.08326" data-arxiv-id="2408.08326" class="link-https">arXiv:2408.08326</a>]. Some other curves for measurements instead of the lines $L$ are also considered. Applications to the Gelfand-Krein-Levitan inverse problem and passive imaging are also indicated. </p> </div> </dd> <dt> <a name='item12'>[12]</a> <a href ="/abs/2411.13605" title="Abstract" id="2411.13605"> arXiv:2411.13605 </a> (cross-list from hep-th) [<a href="/pdf/2411.13605" title="Download PDF" id="pdf-2411.13605" aria-labelledby="pdf-2411.13605">pdf</a>, <a href="https://arxiv.org/html/2411.13605v1" title="View HTML" id="html-2411.13605" aria-labelledby="html-2411.13605" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13605" title="Other formats" id="oth-2411.13605" aria-labelledby="oth-2411.13605">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Quantum Field Measurements in the Fewster-Verch Framework </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Mandrysch,+J">Jan Mandrysch</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Navascu%C3%A9s,+M">Miguel Navascu茅s</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 21 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; Mathematical Physics (math-ph); Quantum Physics (quant-ph) </div> <p class='mathjax'> The Fewster-Verch (FV) framework was introduced as a prescription to define local operations within a quantum field theory (QFT) that are free from Sorkin-like causal paradoxes. In this framework the measurement device is modeled via a probe QFT that, after interacting with the target QFT, is subject to an arbitrary local measurement. While the FV framework is rich enough to carry out quantum state tomography, it has two drawbacks. First, it is unclear if the FV framework allows conducting arbitrary local measurements. Second, if the probe field is interpreted as physical and the FV framework as fundamental, then one must demand the probe measurement to be itself implementable within the framework. That would involve a new probe, which should also be subject to an FV measurement, and so on. It is unknown if there exist non-trivial FV measurements for which such an "FV-Heisenberg cut" can be moved arbitrarily far away. In this work, we advance the first problem by proving that measurements of locally smeared fields fit within the FV framework. We solve the second problem by showing that any such field measurement admits a movable FV-Heisenberg cut. </p> </div> </dd> <dt> <a name='item13'>[13]</a> <a href ="/abs/2411.13606" title="Abstract" id="2411.13606"> arXiv:2411.13606 </a> (cross-list from cond-mat.stat-mech) [<a href="/pdf/2411.13606" title="Download PDF" id="pdf-2411.13606" aria-labelledby="pdf-2411.13606">pdf</a>, <a href="https://arxiv.org/html/2411.13606v1" title="View HTML" id="html-2411.13606" aria-labelledby="html-2411.13606" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13606" title="Other formats" id="oth-2411.13606" aria-labelledby="oth-2411.13606">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The stabilizing role of multiplicative noise in non-confining potentials </div> <div class='list-authors'><a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Phillips,+E+T">Ewan T. Phillips</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Lindner,+B">Benjamin Lindner</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Kantz,+H">Holger Kantz</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 14 pages, 8 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Statistical Mechanics (cond-mat.stat-mech)</span>; Mathematical Physics (math-ph); Statistics Theory (math.ST); Adaptation and Self-Organizing Systems (nlin.AO) </div> <p class='mathjax'> We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly causes the mass of the stationary probability distribution to become increasingly concentrated around the minima of the multiplicative noise term, whilst under quite general conditions exhibiting a kind of intermittent burst like jumps between these minima. If the multiplicative noise term has one zero this causes on-off intermittency. Our framework relies on first term expansions, which become more accurate for larger noise intensities. In this work we show that the full width half maximum in addition to the maximum is appropriate for quantifying the stationary probability distribution (instead of the mean and variance, which are often undefined). We define a corresponding new kind of weak sense stationarity. We consider a double well potential as an example of application, demonstrating relevance to tipping points in noisy systems. </p> </div> </dd> <dt> <a name='item14'>[14]</a> <a href ="/abs/2411.13713" title="Abstract" id="2411.13713"> arXiv:2411.13713 </a> (cross-list from nlin.SI) [<a href="/pdf/2411.13713" title="Download PDF" id="pdf-2411.13713" aria-labelledby="pdf-2411.13713">pdf</a>, <a href="https://arxiv.org/html/2411.13713v1" title="View HTML" id="html-2411.13713" aria-labelledby="html-2411.13713" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13713" title="Other formats" id="oth-2411.13713" aria-labelledby="oth-2411.13713">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Closed-form solutions of the nonlinear Schr\"odinger equation with arbitrary dispersion and potential </div> <div class='list-authors'><a href="https://arxiv.org/search/nlin?searchtype=author&query=Polyanin,+A+D">Andrei D. Polyanin</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=Kudryashov,+N+A">Nikolay A. Kudryashov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 28 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Exactly Solvable and Integrable Systems (nlin.SI)</span>; Mathematical Physics (math-ph); Analysis of PDEs (math.AP) </div> <p class='mathjax'> For the first time, the general nonlinear Schr枚dinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class of related nonlinear partial differential equations that are often used in various areas of theoretical physics, including nonlinear optics, superconductivity and plasma physics. To construct exact solutions, a combination of the method of functional constraints and methods of generalized separation of variables is used. Exact closed-form solutions of the general nonlinear Schr枚dinger equation, which are expressed in quadratures or elementary functions, are found. One-dimensional non-symmetry reductions are described, which lead the considered nonlinear partial differential equation to a simpler ordinary differential equation or a system of such equations. The exact solutions obtained in this work can be used as test problems intended to assess the accuracy of numerical and approximate analytical methods for integrating nonlinear equations of mathematical physics. </p> </div> </dd> <dt> <a name='item15'>[15]</a> <a href ="/abs/2411.13726" title="Abstract" id="2411.13726"> arXiv:2411.13726 </a> (cross-list from math.AP) [<a href="/pdf/2411.13726" title="Download PDF" id="pdf-2411.13726" aria-labelledby="pdf-2411.13726">pdf</a>, <a href="https://arxiv.org/html/2411.13726v1" title="View HTML" id="html-2411.13726" aria-labelledby="html-2411.13726" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13726" title="Other formats" id="oth-2411.13726" aria-labelledby="oth-2411.13726">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A priori estimates for the linearized relativistic Euler equations with a physical vacuum boundary and an ideal gas equation of state </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Luczak,+B+B">Brian B. Luczak</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> In this paper, we will provide a result on the relativistic Euler equations for an ideal gas equation of state and a physical vacuum boundary. More specifically, we will prove a priori estimates for the linearized system in weighted Sobolev spaces. Our focus will be on choosing the correct thermodynamic variables, developing a weighted book-keeping scheme, and then proving energy estimates for the linearized system. </p> </div> </dd> <dt> <a name='item16'>[16]</a> <a href ="/abs/2411.13923" title="Abstract" id="2411.13923"> arXiv:2411.13923 </a> (cross-list from math.PR) [<a href="/pdf/2411.13923" title="Download PDF" id="pdf-2411.13923" aria-labelledby="pdf-2411.13923">pdf</a>, <a href="https://arxiv.org/html/2411.13923v1" title="View HTML" id="html-2411.13923" aria-labelledby="html-2411.13923" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13923" title="Other formats" id="oth-2411.13923" aria-labelledby="oth-2411.13923">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Fourier dimension of Gaussian multiplicative chaos </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Lin,+Z">Zhaofeng Lin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Qiu,+Y">Yanqi Qiu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tan,+M">Mingjie Tan</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> This is the first version of our work on Fourier dimension of GMC. New version with more comprehensive and simpler proof, together with illustrative pictures and applications, generalizations of the main result will be updated soon </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Mathematical Physics (math-ph); Dynamical Systems (math.DS); Functional Analysis (math.FA) </div> <p class='mathjax'> We obtain the precise Fourier dimension of the Gaussian multiplicative chaos on the unit interval. Our main result confirms a conjecture of Garban-Vargas. </p> </div> </dd> <dt> <a name='item17'>[17]</a> <a href ="/abs/2411.14043" title="Abstract" id="2411.14043"> arXiv:2411.14043 </a> (cross-list from quant-ph) [<a href="/pdf/2411.14043" title="Download PDF" id="pdf-2411.14043" aria-labelledby="pdf-2411.14043">pdf</a>, <a href="https://arxiv.org/html/2411.14043v1" title="View HTML" id="html-2411.14043" aria-labelledby="html-2411.14043" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14043" title="Other formats" id="oth-2411.14043" aria-labelledby="oth-2411.14043">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> From classical probability densities to quantum states: quantization of Gaussian for arbitrary orderings </div> <div class='list-authors'><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Giudice,+G+L">Giorgio Lo Giudice</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Leone,+L">Lorenzo Leone</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Lizzi,+F">Fedele Lizzi</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 16 Pages, one figure </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Physics (quant-ph)</span>; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) </div> <p class='mathjax'> The primary focus of this work is to investigate how the most emblematic classical probability density, namely a Gaussian, can be mapped to a valid quantum states. To explore this issue, we consider a Gaussian whose squared variance depends on a parameter $\lambda$. Specifically, depending on the value of $\lambda$, we study what happens in the classical-quantum correspondence as we change the indeterminacy of the classical particle. Furthermore, finding a correspondence between a classical state and a quantum state is not a trivial task. Quantum observables, described by Hermitian operators, do not generally commute, so a precise ordering must be introduced to resolve this ambiguity. In this work, we study two different arbitrary orderings: the first is an arbitrary ordering of the position and momentum observables; the second, which is the main focus of the present work, is an arbitrary ordering of the annihilation and creation operators. In this latter case, we find the interesting result that even a $\delta$-function, which in general has no quantum correspondence, can be mapped into a valid quantum state for a particular ordering, specifically the antinormal one (all creation operators are to the right of all annihilation operators in the product). This means that the Gaussian probability density corresponds to a valid quantum state, regardless of how localized classical particles are in phase space. </p> </div> </dd> <dt> <a name='item18'>[18]</a> <a href ="/abs/2411.14089" title="Abstract" id="2411.14089"> arXiv:2411.14089 </a> (cross-list from gr-qc) [<a href="/pdf/2411.14089" title="Download PDF" id="pdf-2411.14089" aria-labelledby="pdf-2411.14089">pdf</a>, <a href="https://arxiv.org/html/2411.14089v1" title="View HTML" id="html-2411.14089" aria-labelledby="html-2411.14089" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14089" title="Other formats" id="oth-2411.14089" aria-labelledby="oth-2411.14089">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Is there any Trinity of Gravity, to start with? </div> <div class='list-authors'><a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Golovnev,+A">Alexey Golovnev</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages; prepared for Proceedings of 11th Mathematical Physics Meeting, September 2024 in Belgrade, Serbia </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">General Relativity and Quantum Cosmology (gr-qc)</span>; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); History and Philosophy of Physics (physics.hist-ph) </div> <p class='mathjax'> In recent years, it has been rather fashionable to talk about geometric trinity of gravity. The main idea is that one can formally present the gravity equations in different terms, those of either torsion or nonmetricity instead of curvature. It starts from a very erroneous claim that the Levi-Civita connection, and therefore the (pseudo-)Riemannian geometry itself, are nothing but an arbitrary choice. The point is that, as long as we admit the need of having a metric for describing gravity, the standard approach does not involve any additional independent geometric structures on top of that. At the same time, any other metric-affine model does go for genuinely new stuff. In particular, the celebrated teleparallel framework introduces a notion of yet another parallel transport which is flat. It gives us curious new ways of modifying gravity, even though very often quite problematic. However, in GR-equivalent models, we only get a new language for describing the same physics, in terms of absolutely unobservable and unpredictable geometrical inventions. For sure, one can always safely create novel constructions which do not influence the physical equations of motion, but in itself it does not make much sense and blatantly goes against the Occam's razor. </p> </div> </dd> <dt> <a name='item19'>[19]</a> <a href ="/abs/2411.14204" title="Abstract" id="2411.14204"> arXiv:2411.14204 </a> (cross-list from quant-ph) [<a href="/pdf/2411.14204" title="Download PDF" id="pdf-2411.14204" aria-labelledby="pdf-2411.14204">pdf</a>, <a href="https://arxiv.org/html/2411.14204v1" title="View HTML" id="html-2411.14204" aria-labelledby="html-2411.14204" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14204" title="Other formats" id="oth-2411.14204" aria-labelledby="oth-2411.14204">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Exact solution for a class of quantum models of interacting bosons </div> <div class='list-authors'><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Shchesnovich,+V">Valery Shchesnovich</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages, no figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Physics (quant-ph)</span>; Quantum Gases (cond-mat.quant-gas); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI) </div> <p class='mathjax'> Quantum models of interacting bosons have wide range of applications, among them the propagation of optical modes in nonlinear media, such as the $k$-photon down conversion. Many of such models are related to nonlinear deformations of finite group algebras, thus, in this sense, they are exactly solvable. Whereas the advanced group-theoretic methods have been developed to study the eigenvalue spectrum of exactly solvable Hamiltonians, in quantum optics the prime interest is not the spectrum of the Hamiltonian, but the evolution of an initial state, such as the generation of optical signal modes by a strong pump mode propagating in a nonlinear medium. I propose a simple and general method of derivation of the solution to such a state evolution problem, applicable to a wide class of quantum models of interacting bosons. For the $k$-photon down conversion model and its generalizations, the solution to the state evolution problem is given in the form of an infinite series expansion in the powers of propagation time with the coefficients defined by a recursion relation with a single polynomial function, unique for each nonlinear model. As an application, I compare the exact solution to the parametric down conversion process with the semiclassical parametric approximation. </p> </div> </dd> <dt> <a name='item20'>[20]</a> <a href ="/abs/2411.14236" title="Abstract" id="2411.14236"> arXiv:2411.14236 </a> (cross-list from math.PR) [<a href="/pdf/2411.14236" title="Download PDF" id="pdf-2411.14236" aria-labelledby="pdf-2411.14236">pdf</a>, <a href="/format/2411.14236" title="Other formats" id="oth-2411.14236" aria-labelledby="oth-2411.14236">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Size of chaos for Gibbs measures of mean field interacting diffusions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ren,+Z">Zhenjie Ren</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Wang,+S">Songbo Wang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 35 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> We investigate Gibbs measures for diffusive particles interacting through a two-body mean field energy. By uncovering a gradient structure for the conditional law, we derive sharp bounds on the size of chaos, providing a quantitative characterization of particle independence. To handle unbounded interaction forces, we study the concentration of measure phenomenon for Gibbs measures via a defective Talagrand inequality, which may hold independent interest. Our approach provides a unified framework for both the flat semi-convex and displacement convex cases. Additionally, we establish sharp chaos bounds for the quartic Curie-Weiss model in the sub-critical regime, demonstrating the generality of this method. </p> </div> </dd> <dt> <a name='item21'>[21]</a> <a href ="/abs/2411.14261" title="Abstract" id="2411.14261"> arXiv:2411.14261 </a> (cross-list from hep-th) [<a href="/pdf/2411.14261" title="Download PDF" id="pdf-2411.14261" aria-labelledby="pdf-2411.14261">pdf</a>, <a href="https://arxiv.org/html/2411.14261v1" title="View HTML" id="html-2411.14261" aria-labelledby="html-2411.14261" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14261" title="Other formats" id="oth-2411.14261" aria-labelledby="oth-2411.14261">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On braid statistics versus parastatistics </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Toppan,+F">Francesco Toppan</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 11 pages. Based on a plenary talk at ISQS28, Prague, July 1-5, 2024; to appear in the Proceedings </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Quantum Physics (quant-ph) </div> <p class='mathjax'> I report the recent advances in applying (graded) Hopf algebras with braided tensor product in two scenarios: i) paraparticles beyond bosons and fermions living in any space dimensions and transforming under the permutation group; ii) physical models of anyons living in two space-dimensions and transforming under the braid group. In the first scenario simple toy models based on the so-called $2$-bit parastatistics show that, in the multiparticle sector, certain observables can discriminate paraparticles from ordinary bosons/fermions (thus, providing a counterexample to the widespread belief of the "conventionality of parastatistics" argument). In the second scenario the notion of (braided) Majorana qubit is introduced as the simplest building block to implement the Kitaev's proposal of a topological quantum computer which protects from decoherence. </p> </div> </dd> <dt> <a name='item22'>[22]</a> <a href ="/abs/2411.14302" title="Abstract" id="2411.14302"> arXiv:2411.14302 </a> (cross-list from cond-mat.quant-gas) [<a href="/pdf/2411.14302" title="Download PDF" id="pdf-2411.14302" aria-labelledby="pdf-2411.14302">pdf</a>, <a href="https://arxiv.org/html/2411.14302v1" title="View HTML" id="html-2411.14302" aria-labelledby="html-2411.14302" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14302" title="Other formats" id="oth-2411.14302" aria-labelledby="oth-2411.14302">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Electrodynamics of Vortices in Quasi-2D Scalar Bose-Einstein Condensates </div> <div class='list-authors'><a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Shinn,+S">Seong-Ho Shinn</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=del+Campo,+A">Adolfo del Campo</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 15 pages, 1 figure </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Gases (cond-mat.quant-gas)</span>; Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Plasma Physics (physics.plasm-ph); Quantum Physics (quant-ph) </div> <p class='mathjax'> In two spatial dimensions, vortex-vortex interactions approximately vary with the logarithm of the inter-vortex distance, making it possible to describe an ensemble of vortices as a Coulomb gas. We introduce a duality between vortices in a quasi-two-dimensional (quasi-2D) scalar Bose-Einstein condensates (BEC) and effective Maxwell's electrodynamics. Specifically, we address the general scenario of inhomogeneous, time-dependent BEC number density with dissipation or rotation. Starting from the Gross-Pitaevskii equation (GPE), which describes the mean-field dynamics of a quasi-2D scalar BEC without dissipation, we show how to map vortices in a quasi-2D scalar BEC to 2D electrodynamics beyond the point-vortex approximation, even when dissipation is present or in a rotating system. The physical meaning of this duality is discussed. </p> </div> </dd> <dt> <a name='item23'>[23]</a> <a href ="/abs/2411.14329" title="Abstract" id="2411.14329"> arXiv:2411.14329 </a> (cross-list from hep-th) [<a href="/pdf/2411.14329" title="Download PDF" id="pdf-2411.14329" aria-labelledby="pdf-2411.14329">pdf</a>, <a href="https://arxiv.org/html/2411.14329v1" title="View HTML" id="html-2411.14329" aria-labelledby="html-2411.14329" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14329" title="Other formats" id="oth-2411.14329" aria-labelledby="oth-2411.14329">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Peierls substitution and Hall motion in exotic Carroll dynamics </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Zeng,+H">H.-X. Zeng</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Zhao,+Q">Q.-L. Zhao</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Zhang,+P">P.-M. Zhang</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Horvathy,+P+A">P. A. Horvathy</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 29 pages, 2 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> The particle with first-order dynamics proposed by Dunne, Jackiw and Trugenberger (DJT) to justify the "Peierls substitution" is obtained by reduction from both of two-parameter centrally extended Galilean and Carroll systems. In the latter case the extension parameters $\kappa_{exo}$ and $\kappa_{mag}$ generate non-commutativity of the coordinates resp. behave as an internal magnetic field. The position and momentum follow uncoupled anomalous Hall motions. Consistently with partial immobility, one of the Carroll boost generators is broken but the other remains a symmetry. Switching off $\kappa_{exo}$, the immobility of unextended Carroll particles is recovered. The Carroll system is dual to an uncharged anyon on the horizon of a black hole which exhibits the spin-Hall effect. </p> </div> </dd> <dt> <a name='item24'>[24]</a> <a href ="/abs/2411.14334" title="Abstract" id="2411.14334"> arXiv:2411.14334 </a> (cross-list from math.AP) [<a href="/pdf/2411.14334" title="Download PDF" id="pdf-2411.14334" aria-labelledby="pdf-2411.14334">pdf</a>, <a href="https://arxiv.org/html/2411.14334v1" title="View HTML" id="html-2411.14334" aria-labelledby="html-2411.14334" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14334" title="Other formats" id="oth-2411.14334" aria-labelledby="oth-2411.14334">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Well-Posedness for Dean-Kawasaki Models of Vlasov-Fokker-Planck Type </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=M%C3%BCller,+F">Fenna M眉ller</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=von+Renesse,+M">Max von Renesse</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zimmer,+J">Johannes Zimmer</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Mathematical Physics (math-ph); Probability (math.PR) </div> <p class='mathjax'> We consider systems of interacting particles which are described by a second order Langevin equation, i.e., particles experiencing inertia. We introduce an associated equation of fluctuating hydrodynamics, which can be interpreted as stochastic version of a Vlasov-Fokker-Planck equation. We show that this stochastic partial differential equation exhibits the same dichotomy as the corresponding first order (inertial-free) equation, the so-called Dean-Kawasaki equation: Solutions exist only for suitable atomic initial data, but not for smooth initial data. The class of systems covered includes several models of active matter. </p> </div> </dd> <dt> <a name='item25'>[25]</a> <a href ="/abs/2411.14390" title="Abstract" id="2411.14390"> arXiv:2411.14390 </a> (cross-list from cond-mat.dis-nn) [<a href="/pdf/2411.14390" title="Download PDF" id="pdf-2411.14390" aria-labelledby="pdf-2411.14390">pdf</a>, <a href="https://arxiv.org/html/2411.14390v1" title="View HTML" id="html-2411.14390" aria-labelledby="html-2411.14390" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14390" title="Other formats" id="oth-2411.14390" aria-labelledby="oth-2411.14390">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Persistent Homology for Structural Characterization in Disordered Systems </div> <div class='list-authors'><a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Wang,+A">An Wang</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Zou,+L">Li Zou</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 19 pages, 17 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Disordered Systems and Neural Networks (cond-mat.dis-nn)</span>; Materials Science (cond-mat.mtrl-sci); Machine Learning (cs.LG); Mathematical Physics (math-ph); Algebraic Topology (math.AT) </div> <p class='mathjax'> We propose a unified framework based on persistent homology (PH) to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data structure, and has shown to be highly effective and interpretable in predicting particle rearrangements and classifying global phases. Based on this framework, we define a non-parametric metric, the Separation Index (SI), which not only outperforms traditional bond-orientational order parameters in phase classification tasks but also establishes a connection between particle environments and the global phase structure. Our methods provide an effective framework for understanding and analyzing the properties of disordered materials, with broad potential applications in materials science and even wider studies of complex systems. </p> </div> </dd> <dt> <a name='item26'>[26]</a> <a href ="/abs/2411.14396" title="Abstract" id="2411.14396"> arXiv:2411.14396 </a> (cross-list from hep-th) [<a href="/pdf/2411.14396" title="Download PDF" id="pdf-2411.14396" aria-labelledby="pdf-2411.14396">pdf</a>, <a href="/format/2411.14396" title="Other formats" id="oth-2411.14396" aria-labelledby="oth-2411.14396">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Moore,+G+W">Gregory W. Moore</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Saxena,+V">Vivek Saxena</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Singh,+R+K">Ranveer Kumar Singh</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 46 pages + appendices = 97 pages, 4 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; Mathematical Physics (math-ph); Algebraic Topology (math.AT); Differential Geometry (math.DG); Geometric Topology (math.GT) </div> <p class='mathjax'> We discuss what topological data must be provided to define topologically twisted partition functions of four-dimensional $\mathcal{N}=2$ supersymmetric field theories. The original example of Donaldson-Witten theory depends only on the diffeomorphism type of the spacetime and 't Hooft fluxes (characteristic classes of background gerbe connections, a.k.a. "one-form symmetry connections.") The example of $\mathcal{N}=2^*$ theories shows that, in general, the twisted partition functions depend on further topological data. We describe topological twisting for general four-dimensional $\mathcal{N}=2$ theories and argue that the topological partition functions depend on (a): the diffeomorphism type of the spacetime, (b): the characteristic classes of background gerbe connections and (c): a "generalized spin-c structure," a concept we introduce and define. The main ideas are illustrated with both Lagrangian theories and class $\mathcal{S}$ theories. In the case of class $\mathcal{S}$ theories of $A_1$ type, we note that the different $S$-duality orbits of a theory associated with a fixed UV curve $C_{g,n}$ can have different topological data. </p> </div> </dd> <dt> <a name='item27'>[27]</a> <a href ="/abs/2411.14399" title="Abstract" id="2411.14399"> arXiv:2411.14399 </a> (cross-list from math.NA) [<a href="/pdf/2411.14399" title="Download PDF" id="pdf-2411.14399" aria-labelledby="pdf-2411.14399">pdf</a>, <a href="https://arxiv.org/html/2411.14399v1" title="View HTML" id="html-2411.14399" aria-labelledby="html-2411.14399" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14399" title="Other formats" id="oth-2411.14399" aria-labelledby="oth-2411.14399">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> DiscoTEX 1.0: Discontinuous collocation and implicit-turned-explicit (IMTEX) integration symplectic, symmetric numerical algorithms with high order jumps for differential equations II: extension to higher-orders of numerical convergence </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Da+Silva,+L+J+G">Lidia J. Gomes Da Silva</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 15 pages, 5 figures, 2 tables. Second paper of a series of papers. See <a href="http://gr.qc" rel="external noopener nofollow" class="link-external link-http">this http URL</a>:<a href="https://arxiv.org/abs/2401.08758" data-arxiv-id="2401.08758" class="link-https">2401.08758</a> for application of these algorithms to numerical black hole perturbation theory. Comments welcomed. arXiv admin note: text overlap with <a href="https://arxiv.org/abs/2401.08758" data-arxiv-id="2401.08758" class="link-https">arXiv:2401.08758</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span>; Instrumentation and Methods for Astrophysics (astro-ph.IM); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph) </div> <p class='mathjax'> \texttt{DiscoTEX} is a highly accurate numerical algorithm for computing numerical weak-form solutions to distributionally sourced partial differential equations (PDE)s. The aim of this second paper, succeeding \cite{da2024discotex}, is to present its extension up to twelve orders. This will be demonstrated by computing numerical weak-form solutions to the distributionally sourced wave equation and comparing it to its exact solutions. The full details of the numerical scheme at higher orders will be presented. </p> </div> </dd> <dt> <a name='item28'>[28]</a> <a href ="/abs/2411.14417" title="Abstract" id="2411.14417"> arXiv:2411.14417 </a> (cross-list from math.QA) [<a href="/pdf/2411.14417" title="Download PDF" id="pdf-2411.14417" aria-labelledby="pdf-2411.14417">pdf</a>, <a href="/format/2411.14417" title="Other formats" id="oth-2411.14417" aria-labelledby="oth-2411.14417">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Construction of Lie algebra weight system kernel via Vogel algebra </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Khudoteplov,+D">Dmitry Khudoteplov</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lanina,+E">Elena Lanina</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sleptsov,+A">Alexey Sleptsov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 18 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Algebra (math.QA)</span>; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Geometric Topology (math.GT); Representation Theory (math.RT) </div> <p class='mathjax'> We develop a method of constructing a kernel of Lie algebra weight system. A main tool we use in the analysis is Vogel's $\Lambda$ algebra and the surrounding framework. As an example of a developed technique we explicitly provide all Jacobi diagrams lying in the kernel of $\mathfrak{sl}_N$ weight system at low orders. We also discuss consequences of the presence of the kernel in Lie algebra weight systems for detection of correlators in the 3D Chern-Simons topological field theory and for distinguishing of knots by the corresponding quantum knot invariants. </p> </div> </dd> </dl> <dl id='articles'> <h3>Replacement submissions (showing 17 of 17 entries)</h3> <dt> <a name='item29'>[29]</a> <a href ="/abs/2212.03780" title="Abstract" id="2212.03780"> arXiv:2212.03780 </a> (replaced) [<a href="/pdf/2212.03780" title="Download PDF" id="pdf-2212.03780" aria-labelledby="pdf-2212.03780">pdf</a>, <a href="/format/2212.03780" title="Other formats" id="oth-2212.03780" aria-labelledby="oth-2212.03780">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Multiple Landau level filling for a mean field limit of 2D fermions </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=P%C3%A9rice,+D">Denis P茅rice</a></div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Journal of Mathematical Physics volume: 65 number: 2 pages: 021902 year: 2024 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; Quantum Gases (cond-mat.quant-gas); Functional Analysis (math.FA); Quantum Physics (quant-ph) </div> <p class='mathjax'> Motivated by the quantum hall effect, we study N two dimensional interacting fermions in a large magnetic field limit. We work in a bounded domain, ensuring finite degeneracy of the Landau levels. In our regime, several levels are fully filled and inert: the density in these levels is constant. We derive a limiting mean-field and semi classical description of the physics in the last, partially filled Landau level. </p> </div> </dd> <dt> <a name='item30'>[30]</a> <a href ="/abs/2404.01756" title="Abstract" id="2404.01756"> arXiv:2404.01756 </a> (replaced) [<a href="/pdf/2404.01756" title="Download PDF" id="pdf-2404.01756" aria-labelledby="pdf-2404.01756">pdf</a>, <a href="https://arxiv.org/html/2404.01756v3" title="View HTML" id="html-2404.01756" aria-labelledby="html-2404.01756" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2404.01756" title="Other formats" id="oth-2404.01756" aria-labelledby="oth-2404.01756">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Antiparticles in non-relativistic quantum mechanics </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Popov,+A+D">Alexander D. Popov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 18 pages; v3: some clarifications </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph) </div> <p class='mathjax'> Non-relativistic quantum mechanics was originally formulated to describe particles. Using ideas from the geometric quantization approach, we show how the concept of antiparticles can and should be introduced in the non-relativistic case without appealing to quantum field theory. We discuss this in detail using the example of the one-dimensional harmonic oscillator. </p> </div> </dd> <dt> <a name='item31'>[31]</a> <a href ="/abs/2408.11575" title="Abstract" id="2408.11575"> arXiv:2408.11575 </a> (replaced) [<a href="/pdf/2408.11575" title="Download PDF" id="pdf-2408.11575" aria-labelledby="pdf-2408.11575">pdf</a>, <a href="https://arxiv.org/html/2408.11575v2" title="View HTML" id="html-2408.11575" aria-labelledby="html-2408.11575" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2408.11575" title="Other formats" id="oth-2408.11575" aria-labelledby="oth-2408.11575">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Contact Structure and Canonical Equations of Stochastic Vector Bundles </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Zhong,+D">D.Y. Zhong</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Wang,+G">G.Q. Wang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> completely revised </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span> </div> <p class='mathjax'> This paper investigates the geometric structure of stochastic vector bundles. It finds that the probability space of stochastic vector bundles possesses an infinite-order jet structure, enabling a gemetrical analysis of stochastic processes. Furthermore, the paper demonstrates that stochastic vector bundles have a natural contact structure, leading to a decomposition of the tangent space and providing insights into the system's evolution and constraints. Finally, it derives a set of canonical equations for stochastic vector bundles, which resemble Hamilton's equations. These equations are connected to the principle of least action, showing the relation between geometric structure of stochastic system evolution and its tendency to minimize energy consumption. This study provides a valuable geometric framework for analyzing stochastic systems, with potential applications in various fields where probabilistic behavior is crucial. </p> </div> </dd> <dt> <a name='item32'>[32]</a> <a href ="/abs/2410.03153" title="Abstract" id="2410.03153"> arXiv:2410.03153 </a> (replaced) [<a href="/pdf/2410.03153" title="Download PDF" id="pdf-2410.03153" aria-labelledby="pdf-2410.03153">pdf</a>, <a href="https://arxiv.org/html/2410.03153v2" title="View HTML" id="html-2410.03153" aria-labelledby="html-2410.03153" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.03153" title="Other formats" id="oth-2410.03153" aria-labelledby="oth-2410.03153">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Factorization of rational six vertex model partition functions </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Motegi,+K">Kohei Motegi</a></div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Nuclear Physics B, 1009 (2024), 116743 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span>; Combinatorics (math.CO) </div> <p class='mathjax'> We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with the explicit forms of the generalized domain wall boundary partition functions by Belliard-Pimenta-Slavnov, we derive factorization formulas for partition functions under trapezoid boundary which can be viewed as a generalization of triangular boundary. We also discuss an application to emptiness formation probabilities under trapezoid boundary which admit determinant representations. </p> </div> </dd> <dt> <a name='item33'>[33]</a> <a href ="/abs/2411.10610" title="Abstract" id="2411.10610"> arXiv:2411.10610 </a> (replaced) [<a href="/pdf/2411.10610" title="Download PDF" id="pdf-2411.10610" aria-labelledby="pdf-2411.10610">pdf</a>, <a href="https://arxiv.org/html/2411.10610v2" title="View HTML" id="html-2411.10610" aria-labelledby="html-2411.10610" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.10610" title="Other formats" id="oth-2411.10610" aria-labelledby="oth-2411.10610">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Asymptotic expansion of the partition function for $\beta$-ensembles with complex potentials </div> <div class='list-authors'><a href="https://arxiv.org/search/math-ph?searchtype=author&query=Guionnet,+A">Alice Guionnet</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Kozlowski,+K">Karol Kozlowski</a>, <a href="https://arxiv.org/search/math-ph?searchtype=author&query=Little,+A">Alex Little</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 64 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Mathematical Physics (math-ph)</span> </div> <p class='mathjax'> In this work we establish under certain hypotheses the $N \to +\infty$ asymptotic expansion of integrals of the form $$\mathcal{Z}_{N,\Gamma}[V] \, = \, \int_{\Gamma^N} \prod_{ a < b}^{N}(z_a - z_b)^\beta \, \prod_{k=1}^{N} \mathrm{e}^{ - N \beta V(z_k) } \, \mathrm{d}\mathbf{z}$$ where $V \in \mathbb{C}[X]$, $\beta \in 2 \mathbb{N}^*$ is an even integer and $\Gamma \subset \mathbb{C}$ is an unbounded contour such that the integral converges. For even degree, real valued $V$s and when $\Gamma = \mathbb{R}$, it is well known that the large-$N$ expansion is characterised by an equilibrium measure corresponding to the minimiser of an appropriate energy functional. This method bears a structural resemblance with the Laplace method. By contrast, in the complex valued setting we are considering, the analysis structurally resembles the classical steepest-descent method, and involves finding a critical point \textit{and} a steepest descent curve, the latter being a deformation of the original integration contour. More precisely, one minimises a curve-dependent energy functional with respect to measures on the curve and then maximises the energy over an appropriate space of curves. Our analysis deals with the one-cut regime of the associated equilibrium measure. We establish the existence of an all order asymptotic expansion for $\ln \mathcal{Z}_{N,\Gamma}[V]$ and explicitly identify the first few terms. </p> </div> </dd> <dt> <a name='item34'>[34]</a> <a href ="/abs/2209.06079" title="Abstract" id="2209.06079"> arXiv:2209.06079 </a> (replaced) [<a href="/pdf/2209.06079" title="Download PDF" id="pdf-2209.06079" aria-labelledby="pdf-2209.06079">pdf</a>, <a href="https://arxiv.org/html/2209.06079v2" title="View HTML" id="html-2209.06079" aria-labelledby="html-2209.06079" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2209.06079" title="Other formats" id="oth-2209.06079" aria-labelledby="oth-2209.06079">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Effective upper bounds on the number of resonance in potential scattering </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cuenin,+J">Jean-Claude Cuenin</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Revised version </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Mathematika, 2024 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Spectral Theory (math.SP)</span>; Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Functional Analysis (math.FA) </div> <p class='mathjax'> We prove upper bounds on the number of resonances and eigenvalues of Schr枚dinger operators $-\Delta+V$ with complex-valued potentials, where $d\geq 3$ is odd. The novel feature of our upper bounds is that they are \emph{effective}, in the sense that they only depend on an exponentially weighted norm of V. Our main focus is on potentials in the Lorentz space $L^{(d+1)/2,1/2}$, but we also obtain new results for compactly supported or pointwise decaying potentials. The main technical innovation, possibly of independent interest, are singular value estimates for Fourier-extension type operators. The obtained upper bounds not only recover several known results in a unified way, they also provide new bounds for potentials which are not amenable to previous methods. </p> </div> </dd> <dt> <a name='item35'>[35]</a> <a href ="/abs/2309.14553" title="Abstract" id="2309.14553"> arXiv:2309.14553 </a> (replaced) [<a href="/pdf/2309.14553" title="Download PDF" id="pdf-2309.14553" aria-labelledby="pdf-2309.14553">pdf</a>, <a href="/format/2309.14553" title="Other formats" id="oth-2309.14553" aria-labelledby="oth-2309.14553">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Inverse non-linear problem of the long wave run-up on coast </div> <div class='list-authors'><a href="https://arxiv.org/search/physics?searchtype=author&query=Rybkin,+A">Alexei Rybkin</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Pelinovsky,+E">Efim Pelinovsky</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Bobrovnikov,+O">Oleksandr Bobrovnikov</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Palmer,+N">Noah Palmer</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Pniushkova,+E">Ekaterina Pniushkova</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Abramowicz,+D">Daniel Abramowicz</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> To appear in Journal of Ocean Engineering and Marine Energy </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Fluid Dynamics (physics.flu-dyn)</span>; Mathematical Physics (math-ph); Geophysics (physics.geo-ph) </div> <p class='mathjax'> The study of the process of catastrophic tsunami-type waves on the coast makes it possible to determine the destructive force of waves on the coast. In hydrodynamics, the one-dimensional theory of the run-up of non-linear waves on a flat slope has gained great popularity, within which rigorous analytical results have been obtained in the class of non-breaking waves. In general, the result depends on the characteristics of the wave approaching (or generated on) the slope, which is usually not known in the measurements. Here we describe a rigorous method for recovering the initial displacement in a source localised in an inclined power-shaped channel from the characteristics of a moving shoreline. The method uses the generalised Carrier-Greenspan transformation, which allows one-dimensional non-linear shallow-water equations to be reduced to linear ones. The solution is found in terms of Erd茅lyi-Kober integral operator. Numerical verification of our results is presented for the cases of a parabolic bay and an infinite plane beach. </p> </div> </dd> <dt> <a name='item36'>[36]</a> <a href ="/abs/2404.11971" title="Abstract" id="2404.11971"> arXiv:2404.11971 </a> (replaced) [<a href="/pdf/2404.11971" title="Download PDF" id="pdf-2404.11971" aria-labelledby="pdf-2404.11971">pdf</a>, <a href="https://arxiv.org/html/2404.11971v2" title="View HTML" id="html-2404.11971" aria-labelledby="html-2404.11971" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2404.11971" title="Other formats" id="oth-2404.11971" aria-labelledby="oth-2404.11971">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Finite-zone PT-potentials </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Taimanov,+I">I.A. Taimanov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 19 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Spectral Theory (math.SP)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> We give a description of finite-zone PT-potentials in terms of explicit theta functional formulas. </p> </div> </dd> <dt> <a name='item37'>[37]</a> <a href ="/abs/2405.00776" title="Abstract" id="2405.00776"> arXiv:2405.00776 </a> (replaced) [<a href="/pdf/2405.00776" title="Download PDF" id="pdf-2405.00776" aria-labelledby="pdf-2405.00776">pdf</a>, <a href="https://arxiv.org/html/2405.00776v2" title="View HTML" id="html-2405.00776" aria-labelledby="html-2405.00776" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2405.00776" title="Other formats" id="oth-2405.00776" aria-labelledby="oth-2405.00776">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Higher spins and Finsler geometry </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Tomasiello,+A">Alessandro Tomasiello</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 36 pages. v2, published version: minor corrections, added references </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph); Differential Geometry (math.DG) </div> <p class='mathjax'> Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors suggests a possible interpretation in terms of higher-spin fields. We will see here that, at linear level in these fields, the Finsler version of the Ricci tensor leads to the curved-space Fronsdal equation for all spins, plus a Stueckelberg-like coupling. Nonlinear terms can also be systematically analyzed, suggesting a possible interacting structure. No particular choice of spacetime dimension is needed. The Stueckelberg mechanism breaks gauge transformations to a redundancy that does not change the geometry. This creates a serious issue: non-transverse modes are not eliminated, at least for the versions of Finsler dynamics examined in this paper. </p> </div> </dd> <dt> <a name='item38'>[38]</a> <a href ="/abs/2406.02573" title="Abstract" id="2406.02573"> arXiv:2406.02573 </a> (replaced) [<a href="/pdf/2406.02573" title="Download PDF" id="pdf-2406.02573" aria-labelledby="pdf-2406.02573">pdf</a>, <a href="/format/2406.02573" title="Other formats" id="oth-2406.02573" aria-labelledby="oth-2406.02573">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On equivalence of gauge-invariant models for massive integer-spin fields </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Fegebank,+A+J">Arcadia John Fegebank</a>, <a href="https://arxiv.org/search/hep-th?searchtype=author&query=Kuzenko,+S+M">Sergei M. Kuzenko</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 39 pages. This work includes the main results of the unpublished manuscript <a href="https://arxiv.org/abs/2310.00951" data-arxiv-id="2310.00951" class="link-https">arXiv:2310.00951</a>; V2: references and comments added; V3: 46 pages, name of first author changed, comments and new appendix added </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Phys. Rev. D 110, 105014 (2024) </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> There are several approaches to formulate gauge-invariant models for massive integer-spin fields in $d$ dimensions including the following: (i) in terms of symmetric tensor fields $\phi_{\mu_1 \dots \mu_k} $, with $k = s, s-1, \dots , 0$, restricted to be double traceless for $k\geq 4$; and (ii) in terms of a quartet of $traceful$ symmetric tensor fields $\psi_{\mu_1 \dots \mu_k} $, of rank $k=s,s-1,s-2, s-3$. We demonstrate that these formulations in Minkowski space ${\mathbb M}^d$ are equivalent to the gauge-invariant theory for a massive integer-spin field proposed in 1989 by Pashnev. We also make use of the Klishevich-Zinoviev theory in ${\mathbb M}^d$ to derive a unique generalisation of the Singh-Hagen model for a massive integer-spin field in $d>4 $ dimensions. </p> </div> </dd> <dt> <a name='item39'>[39]</a> <a href ="/abs/2407.04756" title="Abstract" id="2407.04756"> arXiv:2407.04756 </a> (replaced) [<a href="/pdf/2407.04756" title="Download PDF" id="pdf-2407.04756" aria-labelledby="pdf-2407.04756">pdf</a>, <a href="https://arxiv.org/html/2407.04756v2" title="View HTML" id="html-2407.04756" aria-labelledby="html-2407.04756" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.04756" title="Other formats" id="oth-2407.04756" aria-labelledby="oth-2407.04756">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On Hamiltonian formulations of the Dirac system </div> <div class='list-authors'><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Juh%C3%A1sz,+B">Bence Juh谩sz</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Gergely,+L+%C3%81">L谩szl贸脕rp谩d Gergely</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Annals of Physics, in press, 35 pages, new section added </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Physics (quant-ph)</span>; General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) </div> <p class='mathjax'> We extend a previously successful discussion of the constrained Schr枚dinger system through the Dirac--Bergmann algorithm to the case of the Dirac field. In order to follow the analogy, first we discuss the classical Dirac field as a spinorial variable, by introducing properly defined momenta and a suitably modified, factor ordered Poisson bracket. According to the Dirac--Bergmann algorithm two second class Hamiltonian constraints emerge, leading to a factor ordered Dirac bracket on the full phase space. This becomes the Poisson bracket on the reduced phase space in the canonical chart adapted to the shell. The Dirac equation is recovered both as consistency condition on the full phase space and as canonical equation on the reduced phase space. Alternatively, considering the Dirac field as odd Grassmann variable, we present the details of the Dirac--Bergmann algorithm (with either left and righ derivatives acting on Grassmann valued superfunctions and involving a different type of generalized Poisson and Dirac brackets). We propose a recipe for the canonical second quantization of all three versions of the generalized Dirac brackets, yielding the correct fundamental anticommutator. </p> </div> </dd> <dt> <a name='item40'>[40]</a> <a href ="/abs/2408.17201" title="Abstract" id="2408.17201"> arXiv:2408.17201 </a> (replaced) [<a href="/pdf/2408.17201" title="Download PDF" id="pdf-2408.17201" aria-labelledby="pdf-2408.17201">pdf</a>, <a href="https://arxiv.org/html/2408.17201v2" title="View HTML" id="html-2408.17201" aria-labelledby="html-2408.17201" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2408.17201" title="Other formats" id="oth-2408.17201" aria-labelledby="oth-2408.17201">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Categorical quantization on K\"ahler manifolds </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Yau,+Y">YuTung Yau</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 22 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Symplectic Geometry (math.SG)</span>; Mathematical Physics (math-ph); Differential Geometry (math.DG) </div> <p class='mathjax'> Generalizing deformation quantizations with separation of variables of a K盲hler manifold $M$, we adopt Fedosov's gluing argument to construct a category $\mathsf{DQ}$, enriched over sheaves of $\mathbb{C}[[\hbar]]$-modules on $M$, as a quantization of the category of Hermitian holomorphic vector bundles over $M$ with morphisms being smooth sections of hom-bundles. <br>We then define quantizable morphisms among objects in $\mathsf{DQ}$, generalizing Chan-Leung-Li's notion [4] of quantizable functions. Upon evaluation of quantizable morphisms at $\hbar = \tfrac{\sqrt{-1}}{k}$, we obtain an enriched category $\mathsf{DQ}_{\operatorname{qu}, k}$. We show that, when $M$ is prequantizable, $\mathsf{DQ}_{\operatorname{qu}, k}$ is equivalent to the category $\mathsf{GQ}$ of holomorphic vector bundles over $M$ with morphisms being holomorphic differential operators, via a functor obtained from Bargmann-Fock actions. </p> </div> </dd> <dt> <a name='item41'>[41]</a> <a href ="/abs/2409.16624" title="Abstract" id="2409.16624"> arXiv:2409.16624 </a> (replaced) [<a href="/pdf/2409.16624" title="Download PDF" id="pdf-2409.16624" aria-labelledby="pdf-2409.16624">pdf</a>, <a href="https://arxiv.org/html/2409.16624v2" title="View HTML" id="html-2409.16624" aria-labelledby="html-2409.16624" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.16624" title="Other formats" id="oth-2409.16624" aria-labelledby="oth-2409.16624">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Removable dynamics in the Nose-Hoover and Moore-Spiegel Oscillators </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Igra,+E">Eran Igra</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Mathematical Physics (math-ph); Classical Analysis and ODEs (math.CA) </div> <p class='mathjax'> We study the dynamics of the Nose-Hoover and Moore-Spiegel Oscillators, and in particular, their topological dynamics. We prove the dynamics of both these systems can be reduced to a flow on a solid torus, with at most a finite number of attracting periodic trajectories. As a consequence, we obtain that every periodic trajectory for the Nose-Hoover and the Moore-Spiegel Oscillators is a Torus knot. </p> </div> </dd> <dt> <a name='item42'>[42]</a> <a href ="/abs/2410.00520" title="Abstract" id="2410.00520"> arXiv:2410.00520 </a> (replaced) [<a href="/pdf/2410.00520" title="Download PDF" id="pdf-2410.00520" aria-labelledby="pdf-2410.00520">pdf</a>, <a href="/format/2410.00520" title="Other formats" id="oth-2410.00520" aria-labelledby="oth-2410.00520">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Stretching of Polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Flandoli,+F">Franco Flandoli</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tahraoui,+Y">Yassine Tahraoui</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Mathematical Physics (math-ph); Analysis of PDEs (math.AP) </div> <p class='mathjax'> The aim of this work is understanding the stretching mechanism of stochastic models of turbulence acting on a simple model of dilute polymers. We consider a turbulent model that is white noise in time and activates frequencies in a shell $N\leq |k|\leq 2N$ and investigate the scaling limit as $N\rightarrow \infty$, under suitable intensity assumption, such that the stretching term has a finite limit covariance. The polymer density equation, initially an SPDE, converges weakly to a limit deterministic equation with a new term. Stationary solutions can be computed and show power law decay in the polymer length. </p> </div> </dd> <dt> <a name='item43'>[43]</a> <a href ="/abs/2410.16402" title="Abstract" id="2410.16402"> arXiv:2410.16402 </a> (replaced) [<a href="/pdf/2410.16402" title="Download PDF" id="pdf-2410.16402" aria-labelledby="pdf-2410.16402">pdf</a>, <a href="https://arxiv.org/html/2410.16402v2" title="View HTML" id="html-2410.16402" aria-labelledby="html-2410.16402" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.16402" title="Other formats" id="oth-2410.16402" aria-labelledby="oth-2410.16402">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking </div> <div class='list-authors'><a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Barad,+R">Ruhanshi Barad</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Tang,+Q">Qicheng Tang</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Zhu,+W">Wei Zhu</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Wen,+X">Xueda Wen</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> are welcome. 32 pages, many figures; v2: Refs added </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Strongly Correlated Electrons (cond-mat.str-el)</span>; Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph) </div> <p class='mathjax'> The global symmetry, either invertible or non-invertible, has been extensively studied in two dimensional conformal field theories in recent years. When the theory is defined on a manifold with open boundaries, however, many interesting conformal boundary conditions will fully or partially break such global symmetry. In this work, we study the effect of symmetry-breaking boundaries or interfaces when the system is out of equilibrium. We show that the boundary or interface symmetry-breaking can be detected by the time evolution of string order parameters, which are constructed from the symmetry operators that implement the symmetry transformations. While the string order parameters are independent of time if the symmetry is preserved over the whole system, they evolve in time in a universal way if the boundary or interface breaks the symmetry. More explicitly, in the presence of boundary or interface symmetry-breaking, the string order parameters decay exponentially in time after a global quantum quench, and decay as a power-law in time after a local quantum quench. We also generalize our study to the case when the string order parameters are defined in a subsystem, which are related to the full counting statistics. It is found there are also universal features in the time evolution of string order parameters in this case. We verify our field theory results by studying the time evolution of these two different types of string order parameters in lattice models. </p> </div> </dd> <dt> <a name='item44'>[44]</a> <a href ="/abs/2410.18044" title="Abstract" id="2410.18044"> arXiv:2410.18044 </a> (replaced) [<a href="/pdf/2410.18044" title="Download PDF" id="pdf-2410.18044" aria-labelledby="pdf-2410.18044">pdf</a>, <a href="https://arxiv.org/html/2410.18044v2" title="View HTML" id="html-2410.18044" aria-labelledby="html-2410.18044" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.18044" title="Other formats" id="oth-2410.18044" aria-labelledby="oth-2410.18044">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Time Evolution in Quantum Mechanics with a Minimal Time Scale </div> <div class='list-authors'><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Doma%C5%84ski,+Z">Ziemowit Doma艅ski</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 24 pages, 5 figures </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Symmetry 16, 1520 (2024) </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Physics (quant-ph)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> The existence of a minimum measurable length scale was suggested by various theories of quantum gravity, string theory and black hole physics. Motivated by this, we examine a quantum theory exhibiting a minimum measurable time scale. We use the Page-Wootters formalism to describe time evolution of a quantum system with the modified commutation relations between the time and frequency operator. Such modification leads to a minimal uncertainty in the measurement of time. This causes breaking of the time-translation symmetry and results in a modified version of the Schr枚dinger equation. A minimal time scale also allows us to introduce a discrete Schr枚dinger equation describing time evolution on a lattice. We show that both descriptions of time evolution are equivalent. We demonstrate the developed theory on a couple simple quantum systems. </p> </div> </dd> <dt> <a name='item45'>[45]</a> <a href ="/abs/2411.12868" title="Abstract" id="2411.12868"> arXiv:2411.12868 </a> (replaced) [<a href="/pdf/2411.12868" title="Download PDF" id="pdf-2411.12868" aria-labelledby="pdf-2411.12868">pdf</a>, <a href="https://arxiv.org/html/2411.12868v2" title="View HTML" id="html-2411.12868" aria-labelledby="html-2411.12868" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.12868" title="Other formats" id="oth-2411.12868" aria-labelledby="oth-2411.12868">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the ill-posedness of kinetic wave equations </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ampatzoglou,+I">Ioakeim Ampatzoglou</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=L%C3%A9ger,+T">Tristan L茅ger</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 24 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Mathematical Physics (math-ph) </div> <p class='mathjax'> In this article we identify a sharp ill-posedness/well-posedness threshold for kinetic wave equations (KWE) derived from quasilinear Schr枚dinger models. We show well-posedness using a collisional averaging estimate proved in our earlier work \cite{AmLe}. Ill-posedness manifests as instantaneous loss of smoothness for well-chosen initial data. We also prove that both the gain-only and full equation share the same well-posedness threhold, thus legitimizing a gain-only approach to solving 4-wave kinetic equations. </p> </div> </dd> </dl> <div class='paging'>Total of 45 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math-ph/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> </div> </div> </div> </main> <footer style="clear: both;"> <div class="columns is-desktop" role="navigation" aria-label="Secondary" style="margin: -0.75em -0.75em 0.75em -0.75em">  <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; 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