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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.03425">arXiv:2406.03425</a> <span> [<a href="https://arxiv.org/pdf/2406.03425">pdf</a>, <a href="https://arxiv.org/format/2406.03425">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> </div> <p class="title is-5 mathjax"> Field Theory Approach to Classical $N$-Particle Systems In and Out of Equilibrium </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Daus%2C+T">Tristan Daus</a>, <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">Elena Kozlikin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.03425v1-abstract-short" style="display: inline;"> We present an approach to solving the evolution of a classical $N$-particle ensemble based on the path integral approach to classical mechanics. This formulation provides a perturbative solution to the Liouville equation in terms of a propagator which can be expanded in a Dyson series. We show that this perturbative expansion exactly corresponds to an iterative solution of the BBGKY-hierarchy in o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.03425v1-abstract-full').style.display = 'inline'; document.getElementById('2406.03425v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.03425v1-abstract-full" style="display: none;"> We present an approach to solving the evolution of a classical $N$-particle ensemble based on the path integral approach to classical mechanics. This formulation provides a perturbative solution to the Liouville equation in terms of a propagator which can be expanded in a Dyson series. We show that this perturbative expansion exactly corresponds to an iterative solution of the BBGKY-hierarchy in orders of the interaction potential. Using the path integral formulation, we perform a Hubbard-Stratonovich transformation (HST) to obtain an effective field theoretic description in terms of macroscopic fields, which contains the full microscopic dynamics of the system in its vertices. Naturally, the HST leads to a new perturbative expansion scheme which contains an infinite order of microscopic interactions already at the lowest order of the perturbative expansion. Our approach can be applied to in and out of equilibrium systems with arbitrary interaction potentials and initial conditions. We show how (unequal-time) cumulants of the Klimontovich phase space densities can be computed within this framework and derive results for density and momentum correlations for a spatially homogeneous system. Under the explicit assumptions for the interaction potential and initial conditions, we show that well-known results related to plasma oscillations and the Jeans instability criterion for gravitational collapse can be recovered in the lowest order perturbative expansion and that both are the effect of the same collective behaviour of the many-body system. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.03425v1-abstract-full').style.display = 'none'; document.getElementById('2406.03425v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">49 pages, 5 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2302.01807">arXiv:2302.01807</a> <span> [<a href="https://arxiv.org/pdf/2302.01807">pdf</a>, <a href="https://arxiv.org/format/2302.01807">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> </div> <p class="title is-5 mathjax"> Ultracold plasmas from strongly anti-correlated Rydberg gases in the Kinetic Field Theory formalism </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">Elena Kozlikin</a>, <a href="/search/cond-mat?searchtype=author&query=Lilow%2C+R">Robert Lilow</a>, <a href="/search/cond-mat?searchtype=author&query=Pauly%2C+M">Martin Pauly</a>, <a href="/search/cond-mat?searchtype=author&query=Schuckert%2C+A">Alexander Schuckert</a>, <a href="/search/cond-mat?searchtype=author&query=Salzinger%2C+A">Andre Salzinger</a>, <a href="/search/cond-mat?searchtype=author&query=Bartelmann%2C+M">Matthias Bartelmann</a>, <a href="/search/cond-mat?searchtype=author&query=Weidem%C3%BCller%2C+M">Matthias Weidem眉ller</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2302.01807v1-abstract-short" style="display: inline;"> The dynamics of correlated systems is relevant in many fields ranging from cosmology to plasma physics. However, they are challenging to predict and understand even for classical systems due to the typically large numbers of particles involved. Here, we study the evolution of an ultracold, correlated many-body system with repulsive interactions and initial correlations set by the Rydberg blockade… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.01807v1-abstract-full').style.display = 'inline'; document.getElementById('2302.01807v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.01807v1-abstract-full" style="display: none;"> The dynamics of correlated systems is relevant in many fields ranging from cosmology to plasma physics. However, they are challenging to predict and understand even for classical systems due to the typically large numbers of particles involved. Here, we study the evolution of an ultracold, correlated many-body system with repulsive interactions and initial correlations set by the Rydberg blockade using the analytical framework of Kinetic Field Theory (KFT). The KFT formalism is based on the path-integral formulation for classical mechanics and was first developed and successfully used in cosmology to describe structure formation in Dark Matter. The theoretical framework offers a high flexibility regarding the initial configuration and interactions between particles and, in addition, is computationally cheap. More importantly, the analytic approach allows us to gain better insight into the processes which dominate the dynamics. In this work we show that KFT can be applied in a much more general context and study the evolution of a correlated ion plasma. We find good agreement between the analytical KFT results for the evolution of the correlation function and results obtained from numerical simulations. We use the correlation functions obtained with KFT to compute the temperature increase in the ionic system due to disorder-induced heating. For certain choices of parameters we observe that the effect can be reversed, leading to correlation cooling. Due to its numerical efficiency as compared to numerical simulations, a detailed study using KFT can help to constrain parameter spaces where disorder-induced heating is minimal in order to reach the regime of strong coupling. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.01807v1-abstract-full').style.display = 'none'; document.getElementById('2302.01807v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2012.05812">arXiv:2012.05812</a> <span> [<a href="https://arxiv.org/pdf/2012.05812">pdf</a>, <a href="https://arxiv.org/format/2012.05812">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1475-7516/2021/06/035">10.1088/1475-7516/2021/06/035 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A first comparison of Kinetic Field Theory with Eulerian Standard Perturbation Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">Elena Kozlikin</a>, <a href="/search/cond-mat?searchtype=author&query=Lilow%2C+R">Robert Lilow</a>, <a href="/search/cond-mat?searchtype=author&query=Fabis%2C+F">Felix Fabis</a>, <a href="/search/cond-mat?searchtype=author&query=Bartelmann%2C+M">Matthias Bartelmann</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2012.05812v2-abstract-short" style="display: inline;"> We present a detailed comparison of the newly developed particle-based Kinetic Field Theory framework for cosmic large-scale structure formation with the established formalism of Eulerian Standard Perturbation Theory. We highlight the qualitative differences of both approaches by a comparative analysis of the respective equations of motion and implementation of initial conditions. A natural starti… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.05812v2-abstract-full').style.display = 'inline'; document.getElementById('2012.05812v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2012.05812v2-abstract-full" style="display: none;"> We present a detailed comparison of the newly developed particle-based Kinetic Field Theory framework for cosmic large-scale structure formation with the established formalism of Eulerian Standard Perturbation Theory. We highlight the qualitative differences of both approaches by a comparative analysis of the respective equations of motion and implementation of initial conditions. A natural starting point for a first quantitative comparison is given by the non-interacting regime of free-streaming kinematics. Our results suggest that Kinetic Field Theory contains a complete resummation of Standard Perturbation Theory in this regime. We further show that the exact free-streaming solution of Kinetic Field Theory can not be recovered in any finite order of Standard Perturbation Theory. Kinetic Field Theory should therefore provide a better starting point for perturbative treatments of non-linear structure formation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.05812v2-abstract-full').style.display = 'none'; document.getElementById('2012.05812v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 December, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JCAP06(2021)035 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1810.13324">arXiv:1810.13324</a> <span> [<a href="https://arxiv.org/pdf/1810.13324">pdf</a>, <a href="https://arxiv.org/format/1810.13324">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> </div> <p class="title is-5 mathjax"> A Model for Hydrodynamics in Kinetic Field Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Viermann%2C+C">C. Viermann</a>, <a href="/search/cond-mat?searchtype=author&query=Schneider%2C+J+T">J. T. Schneider</a>, <a href="/search/cond-mat?searchtype=author&query=Lilow%2C+R">R. Lilow</a>, <a href="/search/cond-mat?searchtype=author&query=Fabis%2C+F">F. Fabis</a>, <a href="/search/cond-mat?searchtype=author&query=Littek%2C+C">C. Littek</a>, <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">E. Kozlikin</a>, <a href="/search/cond-mat?searchtype=author&query=Bartelmann%2C+M">M. Bartelmann</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1810.13324v1-abstract-short" style="display: inline;"> In this work, we introduce an effective model for both ideal and viscous fluid dynamics within the framework of kinetic field theory (KFT). The main application we have in mind is cosmic structure formation where gaseous components need to be gravitationally coupled to dark matter. However, we expect that the fluid model is much more widely applicable. The idea behind the effective model is simila… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1810.13324v1-abstract-full').style.display = 'inline'; document.getElementById('1810.13324v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1810.13324v1-abstract-full" style="display: none;"> In this work, we introduce an effective model for both ideal and viscous fluid dynamics within the framework of kinetic field theory (KFT). The main application we have in mind is cosmic structure formation where gaseous components need to be gravitationally coupled to dark matter. However, we expect that the fluid model is much more widely applicable. The idea behind the effective model is similar to that of smoothed particle hydrodynamics. By introducing mesoscopic particles equipped with a position, a momentum, and an enthalpy, we construct a free theory for such particles and derive suitable interaction operators. We then show that the model indeed leads to the correct macroscopic evolution equations, namely the continuity, Euler, Navier-Stokes, and energy conservation equations of both ideal and viscous hydrodynamics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1810.13324v1-abstract-full').style.display = 'none'; document.getElementById('1810.13324v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 October, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, 1 figure</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1809.06942">arXiv:1809.06942</a> <span> [<a href="https://arxiv.org/pdf/1809.06942">pdf</a>, <a href="https://arxiv.org/format/1809.06942">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1475-7516/2019/04/001">10.1088/1475-7516/2019/04/001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Resummed Kinetic Field Theory: general formalism and linear structure growth from Newtonian particle dynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Lilow%2C+R">Robert Lilow</a>, <a href="/search/cond-mat?searchtype=author&query=Fabis%2C+F">Felix Fabis</a>, <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">Elena Kozlikin</a>, <a href="/search/cond-mat?searchtype=author&query=Viermann%2C+C">Celia Viermann</a>, <a href="/search/cond-mat?searchtype=author&query=Bartelmann%2C+M">Matthias Bartelmann</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1809.06942v2-abstract-short" style="display: inline;"> In earlier work, we have developed a nonequilibrium statistical field theory description of cosmic structure formation, dubbed Kinetic Field Theory (KFT), which is based on the Hamiltonian phase-space dynamics of classical particles and thus remains valid beyond shell-crossing. Here, we present an exact reformulation of the KFT framework that allows to resum an infinite subset of terms appearing i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.06942v2-abstract-full').style.display = 'inline'; document.getElementById('1809.06942v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1809.06942v2-abstract-full" style="display: none;"> In earlier work, we have developed a nonequilibrium statistical field theory description of cosmic structure formation, dubbed Kinetic Field Theory (KFT), which is based on the Hamiltonian phase-space dynamics of classical particles and thus remains valid beyond shell-crossing. Here, we present an exact reformulation of the KFT framework that allows to resum an infinite subset of terms appearing in the original perturbative expansion of KFT. We develop the general formalism of this resummed KFT, including a diagrammatic language for the resummed perturbation theory, and compute the lowest-order results for the power spectra of the dark matter density contrast and momentum density. This allows us to derive analytically how the linear growth of the largest structures emerges from Newtonian particle dynamics alone, which, to our knowledge, is the first time this has been achieved. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.06942v2-abstract-full').style.display = 'none'; document.getElementById('1809.06942v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 September, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">32 pages, 3 figures; changes in v2: improved motivation of the loop expansion scheme, improved discussion of the small-scale behaviour of the power spectrum, changed Figure 2, minor corrections in the remaining manuscript; content matches published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JCAP 04 (2019) 001 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1710.01611">arXiv:1710.01611</a> <span> [<a href="https://arxiv.org/pdf/1710.01611">pdf</a>, <a href="https://arxiv.org/format/1710.01611">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1742-5468/aab850">10.1088/1742-5468/aab850 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Kinetic Field Theory: Exact free evolution of Gaussian phase-space correlations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Fabis%2C+F">Felix Fabis</a>, <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">Elena Kozlikin</a>, <a href="/search/cond-mat?searchtype=author&query=Lilow%2C+R">Robert Lilow</a>, <a href="/search/cond-mat?searchtype=author&query=Bartelmann%2C+M">Matthias Bartelmann</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1710.01611v1-abstract-short" style="display: inline;"> In recent work we developed a description of cosmic large scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial Gaussian correlations between particles have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1710.01611v1-abstract-full').style.display = 'inline'; document.getElementById('1710.01611v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1710.01611v1-abstract-full" style="display: none;"> In recent work we developed a description of cosmic large scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial Gaussian correlations between particles have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate that explicit expressions for phase-space density cumulants of arbitrary $n$-point order, which fully capture the non-linear coupling of free streaming kinematics due to initial correlations, can be obtained from a simple set of Feynman rules. These cumulants will be the foundation for further investigations of interacting perturbation theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1710.01611v1-abstract-full').style.display = 'none'; document.getElementById('1710.01611v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 October, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">32 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Felix Fabis et al J. Stat. Mech. (2018) 043214 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1412.2715">arXiv:1412.2715</a> <span> [<a href="https://arxiv.org/pdf/1412.2715">pdf</a>, <a href="https://arxiv.org/format/1412.2715">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> </div> <p class="title is-5 mathjax"> Non-equilibrium statistical field theory for classical particles: Impact of correlated initial conditions on non-ideal gases </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">Elena Kozlikin</a>, <a href="/search/cond-mat?searchtype=author&query=Fabis%2C+F">Felix Fabis</a>, <a href="/search/cond-mat?searchtype=author&query=Lilow%2C+R">Robert Lilow</a>, <a href="/search/cond-mat?searchtype=author&query=Viermann%2C+C">Celia Viermann</a>, <a href="/search/cond-mat?searchtype=author&query=Bartelmann%2C+M">Matthias Bartelmann</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1412.2715v1-abstract-short" style="display: inline;"> We use the non-equilibrium statistical field theory for classical particles recently developed by Mazenko and Das and Mazenko, together with the free generating functional for particles initially correlated in phase space derived in Bartelmann et al. to study the impact of initial correlations on the equation of state of real gases. We first show that we can reproduce the well known van der Waals… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.2715v1-abstract-full').style.display = 'inline'; document.getElementById('1412.2715v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1412.2715v1-abstract-full" style="display: none;"> We use the non-equilibrium statistical field theory for classical particles recently developed by Mazenko and Das and Mazenko, together with the free generating functional for particles initially correlated in phase space derived in Bartelmann et al. to study the impact of initial correlations on the equation of state of real gases. We first show that we can reproduce the well known van der Waals equation of state for uncorrelated initial conditions using this approach. We then impose correlated initial conditions and study their qualitative and quantitative effect on the equation of state of a van der Waals gas. The correlations impose a significant correction to the pressure of an ideal gas which is an order of magnitude larger than the correction due to particle interactions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.2715v1-abstract-full').style.display = 'none'; document.getElementById('1412.2715v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 December, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, 1 figure</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1412.2572">arXiv:1412.2572</a> <span> [<a href="https://arxiv.org/pdf/1412.2572">pdf</a>, <a href="https://arxiv.org/format/1412.2572">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</span> </div> </div> <p class="title is-5 mathjax"> Non-equilibrium statistical field theory for classical particles: Initially correlated grand canonical ensembles </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Fabis%2C+F">Felix Fabis</a>, <a href="/search/cond-mat?searchtype=author&query=Berg%2C+D">Daniel Berg</a>, <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">Elena Kozlikin</a>, <a href="/search/cond-mat?searchtype=author&query=Bartelmann%2C+M">Matthias Bartelmann</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1412.2572v1-abstract-short" style="display: inline;"> It was recently shown by Bartelmann et al. how correlated initial conditions can be introduced into the statistical field theory for classical particles pioneered by Das and Mazenko. In this paper we extend this development from the canonical to the grand canonical ensemble for a system satisfying statistical homogeneity and isotropy. We do this by translating the probability distribution for the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.2572v1-abstract-full').style.display = 'inline'; document.getElementById('1412.2572v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1412.2572v1-abstract-full" style="display: none;"> It was recently shown by Bartelmann et al. how correlated initial conditions can be introduced into the statistical field theory for classical particles pioneered by Das and Mazenko. In this paper we extend this development from the canonical to the grand canonical ensemble for a system satisfying statistical homogeneity and isotropy. We do this by translating the probability distribution for the initial phase space coordinates of the particles into an easy diagrammatic representation and then using a variant of the Mayer cluster expansion to sum over particle numbers. The grand canonical generating functional is then used in a structured approach to the derivation of the non-interacting cumulants of the two core collective fields, the density $蟻$ and the response field $B$. As a side-product we find several theorems pertaining to these cumulants which will be useful when investigating the interacting regime of the theory in future work. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.2572v1-abstract-full').style.display = 'none'; document.getElementById('1412.2572v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 December, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 15 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1411.2809">arXiv:1411.2809</a> <span> [<a href="https://arxiv.org/pdf/1411.2809">pdf</a>, <a href="https://arxiv.org/format/1411.2809">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.91.062120">10.1103/PhysRevE.91.062120 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Non-equilibrium statistical field theory for classical particles: Basic kinetic theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Viermann%2C+C">Celia Viermann</a>, <a href="/search/cond-mat?searchtype=author&query=Fabis%2C+F">Felix Fabis</a>, <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">Elena Kozlikin</a>, <a href="/search/cond-mat?searchtype=author&query=Lilow%2C+R">Robert Lilow</a>, <a href="/search/cond-mat?searchtype=author&query=Bartelmann%2C+M">Matthias Bartelmann</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1411.2809v2-abstract-short" style="display: inline;"> Recently Mazenko and Das and Mazenko introduced a non-equilibrium field theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1411.2809v2-abstract-full').style.display = 'inline'; document.getElementById('1411.2809v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1411.2809v2-abstract-full" style="display: none;"> Recently Mazenko and Das and Mazenko introduced a non-equilibrium field theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy (BBGKY hierarchy) with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1411.2809v2-abstract-full').style.display = 'none'; document.getElementById('1411.2809v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 June, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 November, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages, 1 figures, Phys. Rev. E, volume 91, June 2015</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1411.0806">arXiv:1411.0806</a> <span> [<a href="https://arxiv.org/pdf/1411.0806">pdf</a>, <a href="https://arxiv.org/format/1411.0806">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Classical Physics">physics.class-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1367-2630/18/4/043020">10.1088/1367-2630/18/4/043020 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A microscopic, non-equilibrium, statistical field theory for cosmic structure formation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Bartelmann%2C+M">Matthias Bartelmann</a>, <a href="/search/cond-mat?searchtype=author&query=Fabis%2C+F">Felix Fabis</a>, <a href="/search/cond-mat?searchtype=author&query=Berg%2C+D">Daniel Berg</a>, <a href="/search/cond-mat?searchtype=author&query=Kozlikin%2C+E">Elena Kozlikin</a>, <a href="/search/cond-mat?searchtype=author&query=Lilow%2C+R">Robert Lilow</a>, <a href="/search/cond-mat?searchtype=author&query=Viermann%2C+C">Celia Viermann</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1411.0806v2-abstract-short" style="display: inline;"> Building upon the recent pioneering work by Mazenko and by Das and Mazenko, we develop a microscopic, non-equilibrium, statistical field theory for initially correlated canonical ensembles of classical microscopic particles obeying Hamiltonian dynamics. Our primary target is cosmic structure formation, where initial Gaussian correlations in phase space are believed to be set by inflation. We give… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1411.0806v2-abstract-full').style.display = 'inline'; document.getElementById('1411.0806v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1411.0806v2-abstract-full" style="display: none;"> Building upon the recent pioneering work by Mazenko and by Das and Mazenko, we develop a microscopic, non-equilibrium, statistical field theory for initially correlated canonical ensembles of classical microscopic particles obeying Hamiltonian dynamics. Our primary target is cosmic structure formation, where initial Gaussian correlations in phase space are believed to be set by inflation. We give an exact expression for the generating functional of this theory and work out suitable approximations. We specify the initial correlations by a power spectrum and derive general expressions for the correlators of the density and the response field. We derive simple closed expressions for the lowest-order contributions to the non-linear cosmological power spectrum, valid for arbitrary wave numbers. We further calculate the bispectrum expected in this theory within these approximations and the power spectrum of cosmic density fluctuations to first order in the gravitational interaction, using a recent improvement of the Zel'dovich approximation. We show that, with a modification motivated by the adhesion approximation, the non-linear growth of the density power spectrum found in numerical simulations of cosmic structure evolution is reproduced well to redshift zero and for arbitrary wave numbers even within first-order perturbation theory. Our results present the first fully analytic calculation of the non-linear power spectrum of cosmic structures. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1411.0806v2-abstract-full').style.display = 'none'; document.getElementById('1411.0806v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 March, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 November, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">48 pages, 5 figures; accepted for publication in the New Journal of Physics; upon referees' requests, combines earlier submissions 1411.0806, 1411.1153 and 1411.1502</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> New J. Phys. 18 (2016) 043020 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <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 class="nav-spaced"> <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"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><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>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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