Nonlinear Sciences

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aria-labelledby="recent-nlin" href="/list/nlin/recent">recent</a> articles</p> <h3>Showing new listings for Friday, 22 November 2024</h3> <div class='paging'>Total of 18 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/nlin/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 3 of 3 entries)</h3> <dt> <a name='item1'>[1]</a> <a href ="/abs/2411.13713" title="Abstract" id="2411.13713"> arXiv:2411.13713 </a> [<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='item2'>[2]</a> <a href ="/abs/2411.13936" title="Abstract" id="2411.13936"> arXiv:2411.13936 </a> [<a href="/pdf/2411.13936" title="Download PDF" id="pdf-2411.13936" aria-labelledby="pdf-2411.13936">pdf</a>, <a href="https://arxiv.org/html/2411.13936v1" title="View HTML" id="html-2411.13936" aria-labelledby="html-2411.13936" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13936" title="Other formats" id="oth-2411.13936" aria-labelledby="oth-2411.13936">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Formation of nonlinear modes in one-dimensional quasiperiodic lattices with a mobility edge </div> <div class='list-authors'><a href="https://arxiv.org/search/nlin?searchtype=author&query=Zezyulin,+D+A">Dmitry A. Zezyulin</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=Alfimov,+G+L">Georgy L. Alfimov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 13 pages, 7 figures; accepted for Phys. Rev. A </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Pattern Formation and Solitons (nlin.PS)</span>; Quantum Gases (cond-mat.quant-gas); Optics (physics.optics) </div> <p class='mathjax'> We investigate the formation of steady states in one-dimensional Bose-Einstein condensates of repulsively interacting ultracold atoms loaded into a quasiperiodic potential created by two incommensurate periodic lattices. We study the transformations between linear and nonlinear modes and describe the general patterns that govern the birth of nonlinear modes emerging in spectral gaps near band edges. We show that nonlinear modes in a symmetric potential undergo both symmetry-breaking pitchfork bifurcations and saddle-node bifurcations, mimicking the prototypical behaviors of symmetric and asymmetric double-well potentials. The properties of the nonlinear modes differ for bifurcations occurring below and above the mobility edge. In the generic case, when the quasiperiodic potential consists of two incommensurate lattices with a nonzero phase shift between them, the formation of localized modes in the spectral gaps occurs through a cascade of saddle-node bifurcations. Because of the analogy between the Gross-Pitaevskii equation and the nonlinear Schr枚dinger equation, our results can also be applied to optical modes guided by quasiperiodic photonic lattices. </p> </div> </dd> <dt> <a name='item3'>[3]</a> <a href ="/abs/2411.14160" title="Abstract" id="2411.14160"> arXiv:2411.14160 </a> [<a href="/pdf/2411.14160" title="Download PDF" id="pdf-2411.14160" aria-labelledby="pdf-2411.14160">pdf</a>, <a href="https://arxiv.org/html/2411.14160v1" title="View HTML" id="html-2411.14160" aria-labelledby="html-2411.14160" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14160" title="Other formats" id="oth-2411.14160" aria-labelledby="oth-2411.14160">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Breather bound states in a parametrically driven magnetic wire </div> <div class='list-authors'><a href="https://arxiv.org/search/nlin?searchtype=author&query=Castro,+C+J">Camilo Jose Castro</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=Ortega-Piwonka,+I">Ignacio Ortega-Piwonka</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=Malomed,+B+A">Boris A. Malomed</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=Urzagasti,+D">Deterlino Urzagasti</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=Pedraja-Rejas,+L">Liliana Pedraja-Rejas</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=D%C3%ADaz,+P">Pablo D铆az</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=Laroze,+D">David Laroze</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Pattern Formation and Solitons (nlin.PS)</span> </div> <p class='mathjax'> We report the results of systematic investigation of localized dynamical states in the model of a one-dimensional magnetic wire, which is based on the Landau-Lifshitz-Gilbert (LLG) equation. The dissipative term in the LLG equation is compensated by the parametric drive imposed by the external AC magnetic field, which is uniformly applied perpendicular to the rectilinear wire. The existence and stability of the localized states is studied in the plane of the relevant control parameters, viz., the amplitude of the driving term and the detuning of its frequency from the parametric resonance. With the help of systematically performed simulations of the LLG equation, existence and stability areas are identified in the parameter plane for several species of the localized states: stationary single- and two-soliton modes, single and double breathers, drifting double breathers with spontaneously broken inner symmetry, and multi-soliton complexes. Multistability occurs in this system. The breathers emit radiation waves (which explains their drift caused by the spontaneous symmetry breaking, as it breaks the balance between the recoil from the waves emitted to left and right), while the multi-soliton complexes exhibit cycles of periodic transitions between three-, five-, and seven-soliton configurations. Dynamical characteristics of the localized states are systematically calculated too. These include, in particular, the average velocity of the asymmetric drifting modes, and the largest Lyapunov exponent, whose negative and positive values imply that the intrinsic dynamics of the respective modes is regular or chaotic, respectively. </p> </div> </dd> </dl> <dl id='articles'> <h3>Cross submissions (showing 10 of 10 entries)</h3> <dt> <a name='item4'>[4]</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='item5'>[5]</a> <a href ="/abs/2411.13629" title="Abstract" id="2411.13629"> arXiv:2411.13629 </a> (cross-list from cond-mat.stat-mech) [<a href="/pdf/2411.13629" title="Download PDF" id="pdf-2411.13629" aria-labelledby="pdf-2411.13629">pdf</a>, <a href="https://arxiv.org/html/2411.13629v1" title="View HTML" id="html-2411.13629" aria-labelledby="html-2411.13629" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13629" title="Other formats" id="oth-2411.13629" aria-labelledby="oth-2411.13629">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Generalization of the Gauss Map: A jump into chaos with universal features </div> <div class='list-authors'><a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Beck,+C">Christian Beck</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Tirnakli,+U">Ugur Tirnakli</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Tsallis,+C">Constantino Tsallis</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> accepted for publication in PRE </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Statistical Mechanics (cond-mat.stat-mech)</span>; Chaotic Dynamics (nlin.CD) </div> <p class='mathjax'> The Gauss map (or continued fraction map) is an important dissipative one-dimensional discrete-time dynamical system that exhibits chaotic behaviour and which generates a symbolic dynamics consisting of infinitely many different symbols. Here we introduce a generalization of the Gauss map which is given by $x_{t+1}=\frac{1}{x_t^\alpha} - \Bigl[\frac{1}{x_t^\alpha} \Bigr]$ where $\alpha \geq 0$ is a parameter and $x_t \in [0,1]$ ($t=0,1,2,3,\ldots$). The symbol $[\dots ]$ denotes the integer part. This map reduces to the ordinary Gauss map for $\alpha=1$. The system exhibits a sudden `jump into chaos' at the critical parameter value $\alpha=\alpha_c \equiv 0.241485141808811\dots$ which we analyse in detail in this paper. Several analytical and numerical results are established for this new map as a function of the parameter $\alpha$. In particular, we show that, at the critical point, the invariant density approaches a $q$-Gaussian with $q=2$ (i.e., the Cauchy distribution), which becomes infinitely narrow as $\alpha \to \alpha_c^+$. Moreover, in the chaotic region for large values of the parameter $\alpha$ we analytically derive approximate formulas for the invariant density, by solving the corresponding Perron-Frobenius equation. For $\alpha \to \infty$ the uniform density is approached. We provide arguments that some features of this transition scenario are universal and are relevant for other, more general systems as well. </p> </div> </dd> <dt> <a name='item6'>[6]</a> <a href ="/abs/2411.13792" title="Abstract" id="2411.13792"> arXiv:2411.13792 </a> (cross-list from q-fin.PM) [<a href="/pdf/2411.13792" title="Download PDF" id="pdf-2411.13792" aria-labelledby="pdf-2411.13792">pdf</a>, <a href="https://arxiv.org/html/2411.13792v1" title="View HTML" id="html-2411.13792" aria-labelledby="html-2411.13792" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13792" title="Other formats" id="oth-2411.13792" aria-labelledby="oth-2411.13792">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Multiscale Markowitz </div> <div class='list-authors'><a href="https://arxiv.org/search/q-fin?searchtype=author&query=Nayar,+R">Revant Nayar</a>, <a href="https://arxiv.org/search/q-fin?searchtype=author&query=Douady,+R">Raphael Douady</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Portfolio Management (q-fin.PM)</span>; Chaotic Dynamics (nlin.CD); Mathematical Finance (q-fin.MF) </div> <p class='mathjax'> Traditional Markowitz portfolio optimization constrains daily portfolio variance to a target value, optimising returns, Sharpe or variance within this constraint. However, this approach overlooks the relationship between variance at different time scales, typically described by $\sigma(\Delta t) \propto (\Delta t)^{H}$ where $H$ is the Hurst exponent, most of the time assumed to be $\frac{1}{2}$. This paper introduces a multifrequency optimization framework that allows investors to specify target portfolio variance across a range of frequencies, characterized by a target Hurst exponent $H_{target}$, or optimize the portfolio at multiple time scales. By incorporating this scaling behavior, we enable a more nuanced and comprehensive risk management strategy that aligns with investor preferences at various time scales. This approach effectively manages portfolio risk across multiple frequencies and adapts to different market conditions, providing a robust tool for dynamic asset allocation. This overcomes some of the traditional limitations of Markowitz, when it comes to dealing with crashes, regime changes, volatility clustering or multifractality in markets. We illustrate this concept with a toy example and discuss the practical implementation for assets with varying scaling behaviors. </p> </div> </dd> <dt> <a name='item7'>[7]</a> <a href ="/abs/2411.13928" title="Abstract" id="2411.13928"> arXiv:2411.13928 </a> (cross-list from hep-th) [<a href="/pdf/2411.13928" title="Download PDF" id="pdf-2411.13928" aria-labelledby="pdf-2411.13928">pdf</a>, <a href="https://arxiv.org/html/2411.13928v1" title="View HTML" id="html-2411.13928" aria-labelledby="html-2411.13928" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13928" title="Other formats" id="oth-2411.13928" aria-labelledby="oth-2411.13928">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Rational Ruijsenaars-Schneider model with cosmological constant </div> <div class='list-authors'><a href="https://arxiv.org/search/hep-th?searchtype=author&query=Galajinsky,+A">Anton Galajinsky</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 14 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">High Energy Physics - Theory (hep-th)</span>; Exactly Solvable and Integrable Systems (nlin.SI) </div> <p class='mathjax'> The Ruijsenaars-Schneider models are integrable dynamical realizations of the Poincare group in 1+1 dimensions, which reduce to the Calogero and Sutherland systems in the nonrelativistic limit. In this work, a possibility to construct a one-parameter deformation of the Ruijsenaars-Schneider models by uplifting the Poincare algebra in 1+1 dimensions to the anti de Sitter algebra is studied. It is shown that amendments including a cosmological constant are feasible for the rational variant, while the hyperbolic and trigonometric systems are ruled out by our analysis. The issue of integrability of the deformed rational model is discussed in some detail. A complete proof of integrability remains a challenge. </p> </div> </dd> <dt> <a name='item8'>[8]</a> <a href ="/abs/2411.13938" title="Abstract" id="2411.13938"> arXiv:2411.13938 </a> (cross-list from cond-mat.quant-gas) [<a href="/pdf/2411.13938" title="Download PDF" id="pdf-2411.13938" aria-labelledby="pdf-2411.13938">pdf</a>, <a href="https://arxiv.org/html/2411.13938v1" title="View HTML" id="html-2411.13938" aria-labelledby="html-2411.13938" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.13938" title="Other formats" id="oth-2411.13938" aria-labelledby="oth-2411.13938">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Ground-state phase transitions in spin-1 Bose-Einstein condensates with spin-orbit coupling </div> <div class='list-authors'><a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Zhang,+X">Xin-Feng Zhang</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Liu,+Y">Yuan-Fen Liu</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Luo,+H">Huan-Bo Luo</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Liu,+B">Bin Liu</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Dou,+F">Fu-Quan Dou</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Li,+Y">Yongyao Li</a>, <a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Malomed,+B+A">Boris A. Malomed</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> to be published in Physical Review A </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Gases (cond-mat.quant-gas)</span>; Pattern Formation and Solitons (nlin.PS) </div> <p class='mathjax'> We investigate phase transitions of the ground state (GS) of spin-1 Bose-Einstein condensates under the combined action of the spin-orbit coupling (SOC) and gradient magnetic field. Introducing appropariate raising and lowering operators, we exactly solve the linear system. Analyzing the obtained energy spectrum, we conclude that simultaneous variation of the magnetic-field gradient and SOC strength leads to the transition of excited states into the GS. As a result, any excited state can transition to the GS, at appropriate values of the system's parameters. The nonlinear system is solved numerically, showing that the GS phase transition, similar to the one in the linear system, still exists under the action of the repulsive nonlinearity. In the case of weak attraction, a mixed state appears near the GS transition point, while the GS transitions into an edge state under the action of strong attractive interaction. </p> </div> </dd> <dt> <a name='item9'>[9]</a> <a href ="/abs/2411.14015" title="Abstract" id="2411.14015"> arXiv:2411.14015 </a> (cross-list from math-ph) [<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='item10'>[10]</a> <a href ="/abs/2411.14132" title="Abstract" id="2411.14132"> arXiv:2411.14132 </a> (cross-list from math.DS) [<a href="/pdf/2411.14132" title="Download PDF" id="pdf-2411.14132" aria-labelledby="pdf-2411.14132">pdf</a>, <a href="https://arxiv.org/html/2411.14132v1" title="View HTML" id="html-2411.14132" aria-labelledby="html-2411.14132" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14132" title="Other formats" id="oth-2411.14132" aria-labelledby="oth-2411.14132">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Transients versus network interactions give rise to multistability through trapping mechanism </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Rossi,+K+L">Kalel L. Rossi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Medeiros,+E+S">Everton S. Medeiros</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ashwin,+P">Peter Ashwin</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Feudel,+U">Ulrike Feudel</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Submitted to Chaos </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Chaotic Dynamics (nlin.CD) </div> <p class='mathjax'> In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients that give rise to multistability from such interplay remain poorly understood. In a network of coupled excitable units, we show that this interplay generating multistability occurs through a competition between the units' transient dynamics and their coupling. Specifically, the diffusive coupling between the units manages to reinject them in the excitability region of their individual state space and effectively trap them there. We show that this trapping mechanism leads to the coexistence of multiple types of oscillations: periodic, quasiperiodic, and even chaotic, although the units separately do not oscillate. Interestingly, we show that the attractors emerge through different types of bifurcations - in particular, the periodic attractors emerge through either saddle-node of limit cycles bifurcations or homoclinic bifurcations - but in all cases the reinjection mechanism is present. </p> </div> </dd> <dt> <a name='item11'>[11]</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='item12'>[12]</a> <a href ="/abs/2411.14297" title="Abstract" id="2411.14297"> arXiv:2411.14297 </a> (cross-list from math.DS) [<a href="/pdf/2411.14297" title="Download PDF" id="pdf-2411.14297" aria-labelledby="pdf-2411.14297">pdf</a>, <a href="https://arxiv.org/html/2411.14297v1" title="View HTML" id="html-2411.14297" aria-labelledby="html-2411.14297" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14297" title="Other formats" id="oth-2411.14297" aria-labelledby="oth-2411.14297">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Limitations of the Generalized Pareto Distribution-based estimators for the local dimension </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=del+Amo,+I">Ignacio del Amo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Datseris,+G">George Datseris</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Holland,+M">Mark Holland</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Chaotic Dynamics (nlin.CD) </div> <p class='mathjax'> Two dynamical indicators, the local dimension and the extremal index, used to quantify persistence in phase space have been developed and applied to different data across various disciplines. These are computed using the asymptotic limit of exceedances over a threshold, which turns to be a Generalized Pareto Distribution in many cases. However the derivation of the asymptotic distribution requires mathematical properties which are not present even in highly idealized dynamical systems, and unlikely to be present in real data. Here we examine in detail issues that arise when estimating these quantities for some known dynamical systems with a particular focus on how the geometry of an invariant set can affect the regularly varying properties of the invariant measure. We demonstrate that singular measures supported on sets of non-integer dimension are typically not regularly varying and that the absence of regular variation makes the estimates resolution dependent. We show as well that the most common extremal index estimation method is ambiguous for continuous time processes sampled at fixed time steps, which is an underlying assumption in its application to data. </p> </div> </dd> <dt> <a name='item13'>[13]</a> <a href ="/abs/2411.14410" title="Abstract" id="2411.14410"> arXiv:2411.14410 </a> (cross-list from physics.optics) [<a href="/pdf/2411.14410" title="Download PDF" id="pdf-2411.14410" aria-labelledby="pdf-2411.14410">pdf</a>, <a href="https://arxiv.org/html/2411.14410v1" title="View HTML" id="html-2411.14410" aria-labelledby="html-2411.14410" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.14410" title="Other formats" id="oth-2411.14410" aria-labelledby="oth-2411.14410">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Engineering spectro-temporal light states with physics-trained deep learning </div> <div class='list-authors'><a href="https://arxiv.org/search/physics?searchtype=author&query=Liu,+S">Shilong Liu</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Virally,+S">St茅phane Virally</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Demontigny,+G">Gabriel Demontigny</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Cusson,+P">Patrick Cusson</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Seletskiy,+D+V">Denis V. Seletskiy</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Welcome to place your comments </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optics (physics.optics)</span>; Pattern Formation and Solitons (nlin.PS); Classical Physics (physics.class-ph); Quantum Physics (quant-ph) </div> <p class='mathjax'> Frequency synthesis and spectro-temporal control of optical wave packets are central to ultrafast science, with supercontinuum (SC) generation standing as one remarkable example. Through passive manipulation, femtosecond (fs) pulses from nJ-level lasers can be transformed into octave-spanning spectra, supporting few-cycle pulse outputs when coupled with external pulse compressors. While strategies such as machine learning have been applied to control the SC's central wavelength and bandwidth, their success has been limited by the nonlinearities and strong sensitivity to measurement noise. Here, we propose and demonstrate how a physics-trained convolutional neural network (P-CNN) can circumvent such challenges, showing few-fold speedups over the direct approaches. We highlight three key advancements enabled by the P-CNN approach: (i) on-demand control over spectral features of SC, (ii) direct generation of sub-3-cycle pulses from the highly nonlinear fiber, and (iii) the production of high-order solitons, capturing distinct "breather" dynamics in both spectral and temporal domains. This approach heralds a new era of arbitrary spectro-temporal state engineering, with transformative implications for ultrafast and quantum science. </p> </div> </dd> </dl> <dl id='articles'> <h3>Replacement submissions (showing 5 of 5 entries)</h3> <dt> <a name='item14'>[14]</a> <a href ="/abs/2409.04322" title="Abstract" id="2409.04322"> arXiv:2409.04322 </a> (replaced) [<a href="/pdf/2409.04322" title="Download PDF" id="pdf-2409.04322" aria-labelledby="pdf-2409.04322">pdf</a>, <a href="https://arxiv.org/html/2409.04322v2" title="View HTML" id="html-2409.04322" aria-labelledby="html-2409.04322" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2409.04322" title="Other formats" id="oth-2409.04322" aria-labelledby="oth-2409.04322">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Integrability of polynomial vector fields and a dual problem </div> <div class='list-authors'><a href="https://arxiv.org/search/nlin?searchtype=author&query=Petek,+T">Tatjana Petek</a>, <a href="https://arxiv.org/search/nlin?searchtype=author&query=Romanovski,+V">Valery Romanovski</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Exactly Solvable and Integrable Systems (nlin.SI)</span>; Classical Analysis and ODEs (math.CA); Dynamical Systems (math.DS) </div> <p class='mathjax'> We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality the case of quadratic vector fields is considered in detail. </p> </div> </dd> <dt> <a name='item15'>[15]</a> <a href ="/abs/2310.14244" title="Abstract" id="2310.14244"> arXiv:2310.14244 </a> (replaced) [<a href="/pdf/2310.14244" title="Download PDF" id="pdf-2310.14244" aria-labelledby="pdf-2310.14244">pdf</a>, <a href="https://arxiv.org/html/2310.14244v2" title="View HTML" id="html-2310.14244" aria-labelledby="html-2310.14244" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2310.14244" title="Other formats" id="oth-2310.14244" aria-labelledby="oth-2310.14244">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Exact semiclassical dynamics of generic Lipkin-Meshkov-Glick model </div> <div class='list-authors'><a href="https://arxiv.org/search/cond-mat?searchtype=author&query=Yu,+D">Dongyang Yu</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 12 pages, 10 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Gases (cond-mat.quant-gas)</span>; Exactly Solvable and Integrable Systems (nlin.SI) </div> <p class='mathjax'> Lipkin-Meshkov-Glick model is paradigmatic to study quantum phase transition in equilibrium or non-equilibrium systems and entanglement dynamics for a variety of disciplines. In thermodynamics limit, quantum fluctuations are negligible, its semiclassical dynamics in presence of only one nonlinear couplings, as a good benchmark to study quantum fluctuation in finite-size system, can be well obtained in terms of Jacobi elliptic functions. In this work, we extend this semiclassical analysis into the regime where both nonlinear interactions are present, and successfully obtain its exact solutions of semiclassical equations by constructing an auxiliary function that is a linear combination of the $y$ and $z$ component of the classical spin in thermodynamic limit. Taking implementation of Lipkin-Meshkov-Glick model in a Bose-Einstein condensate setup as an example, we figure out all classical dynamical modes, specially find out mesoscopic self-trapping mode in population and phase-difference space even persists in presence of both nonlinear couplings. Our results would be useful to analyze dynamical phase transitions and entanglement dynamics of Lipkin-Meshkov-Glick model in presence of both nonlinear couplings. </p> </div> </dd> <dt> <a name='item16'>[16]</a> <a href ="/abs/2403.14807" title="Abstract" id="2403.14807"> arXiv:2403.14807 </a> (replaced) [<a href="/pdf/2403.14807" title="Download PDF" id="pdf-2403.14807" aria-labelledby="pdf-2403.14807">pdf</a>, <a href="https://arxiv.org/html/2403.14807v2" title="View HTML" id="html-2403.14807" aria-labelledby="html-2403.14807" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2403.14807" title="Other formats" id="oth-2403.14807" aria-labelledby="oth-2403.14807">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Exact Hidden Markovian Dynamics in Quantum Circuits </div> <div class='list-authors'><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Wang,+H">He-Ran Wang</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Yang,+X">Xiao-Yang Yang</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Wang,+Z">Zhong Wang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 7+11 pages, 2+1 figures </div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> Phys. Rev. Lett. 133, 170402 (2024) </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Physics (quant-ph)</span>; Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Exactly Solvable and Integrable Systems (nlin.SI) </div> <p class='mathjax'> Characterizing nonequilibrium dynamics in quantum many-body systems is a challenging frontier of physics. In this Letter, we systematically construct solvable nonintegrable quantum circuits that exhibit exact hidden Markovian subsystem dynamics. This feature thus enables accurately calculating local observables for arbitrary evolution time. Utilizing the influence matrix method, we show that the influence of the time-evolved global system on a finite subsystem can be analytically described by sequential, time-local quantum channels acting on the subsystem with an ancilla of finite Hilbert space dimension. The realization of exact hidden Markovian property is facilitated by a solvable condition on the underlying two-site gates in the quantum circuit. We further present several concrete examples with varying local Hilbert space dimensions to demonstrate our approach. </p> </div> </dd> <dt> <a name='item17'>[17]</a> <a href ="/abs/2404.10224" title="Abstract" id="2404.10224"> arXiv:2404.10224 </a> (replaced) [<a href="/pdf/2404.10224" title="Download PDF" id="pdf-2404.10224" aria-labelledby="pdf-2404.10224">pdf</a>, <a href="https://arxiv.org/html/2404.10224v2" title="View HTML" id="html-2404.10224" aria-labelledby="html-2404.10224" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2404.10224" title="Other formats" id="oth-2404.10224" aria-labelledby="oth-2404.10224">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Prethermalization in aperiodically driven classical spin systems </div> <div class='list-authors'><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Kumar,+S">Sajag Kumar</a>, <a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Choudhury,+S">Sayan Choudhury</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Main Text (6 pages + 3 figures) + Supplementary Material (7 Pages + 11 figures) </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Quantum Physics (quant-ph)</span>; Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Chaotic Dynamics (nlin.CD) </div> <p class='mathjax'> Periodically driven classical many-body systems can host a rich zoo of prethermal dynamical phases. In this work, we extend the paradigm of classical prethermalization to aperiodically driven systems. We establish the existence of a long-lived prethermal regime in spin systems subjected to random multipolar drives (RMDs). We demonstrate that the thermalization time scales as $(1/T)^{2n+2}$, where $n$ is the multipolar order and $T$ is the intrinsic time-scale associated with the drive. In the $n \rightarrow \infty$ limit, the drive becomes quasi-periodic and the thermalization time becomes exponentially long ($\sim \exp(\beta/T)$). We further establish the robustness of prethermalization by demonstrating that these thermalization time scaling laws hold for a wide range of initial state energy densities. Intriguingly, the thermalization process in these classical systems is parametrically slower than their quantum counterparts, thereby highlighting important differences between classical and quantum prethermalization. Finally, we propose a protocol to harness this classical prethermalization to realize time rondeau crystals. </p> </div> </dd> <dt> <a name='item18'>[18]</a> <a href ="/abs/2408.05384" title="Abstract" id="2408.05384"> arXiv:2408.05384 </a> (replaced) [<a href="/pdf/2408.05384" title="Download PDF" id="pdf-2408.05384" aria-labelledby="pdf-2408.05384">pdf</a>, <a href="https://arxiv.org/html/2408.05384v2" title="View HTML" id="html-2408.05384" aria-labelledby="html-2408.05384" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2408.05384" title="Other formats" id="oth-2408.05384" aria-labelledby="oth-2408.05384">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Nonlinear Propagation of Non-Gaussian Uncertainties </div> <div class='list-authors'><a href="https://arxiv.org/search/physics?searchtype=author&query=Acciarini,+G">Giacomo Acciarini</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Baresi,+N">Nicola Baresi</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Lloyd,+D">David Lloyd</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Izzo,+D">Dario Izzo</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Space Physics (physics.space-ph)</span>; Symbolic Computation (cs.SC); Probability (math.PR); Chaotic Dynamics (nlin.CD) </div> <p class='mathjax'> This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions, our approach leverages the relationship between MGFs and distribution moments to extend high-order uncertainty propagation techniques to non-Gaussian scenarios. This significantly broadens the applicability of these methods to a wider range of problems and uncertainty types. High-order moment computations are performed one-off and symbolically, reducing the computational burden of the technique to the calculation of Taylor series coefficients around a nominal trajectory, achieved by efficiently integrating the system's variational equations. Furthermore, the use of the proposed approach in combination with event transition tensors, allows for accurate propagation of uncertainties at specific events, such as the landing surface of a celestial body, the crossing of a predefined Poincar茅 section, or the trigger of an arbitrary event during the propagation. Via numerical simulations we demonstrate the effectiveness of our method in various astrodynamics applications, including the unperturbed and perturbed two-body problem, and the circular restricted three-body problem, showing that it accurately propagates non-Gaussian uncertainties both at future times and at event manifolds. </p> </div> </dd> </dl> <div class='paging'>Total of 18 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/nlin/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; 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