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Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffusive limit. The limit model possesses a formal gradient-flow…

Analysis of PDEs · Mathematics 2017-04-11 Marcel Braukhoff , Ansgar Jüngel

We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The…

Statistical Mechanics · Physics 2009-11-10 Bertrand Lods , Giuseppe Toscani

A non--equilibrium occupation distribution relaxes towards the Fermi--Dirac distribution due to electron--electron scattering even in finite Fermi systems. The dynamic evolution of this thermalization process assumed to result from an…

Disordered Systems and Neural Networks · Physics 2007-05-23 Imre Varga , Peter Thomas , Torsten Meier , Stephan W. Koch

Non-adiabatic molecular phenomena, arising from the breakdown of the Born-Oppenheimer approximation, govern the fate of virtually all photo-physical and photochemical processes and limit the quantum efficiency of molecules and other…

Quantum Physics · Physics 2024-05-15 N. S. Bassler , M. Reitz , R. Holzinger , A. Vibók , G. J. Halász , B. Gurlek , C. Genes

Atoms in high-finesse optical resonators interact via the photons they multiply scatter into the cavity modes. The dynamics is characterized by dispersive and dissipative optomechanical long-range forces, which are mediated by the cavity…

Quantum Physics · Physics 2017-06-13 Tim Keller , Simon B. Jäger , Giovanna Morigi

We study an ultracold gas of neutral atoms subject to the periodic optical potential generated by a high-$Q$ cavity mode. In the limit of very low temperatures, cavity field and atomic dynamics require a quantum description. Starting from a…

Quantum Physics · Physics 2008-02-15 Christoph Maschler , Igor B. Mekhov , Helmut Ritsch

Ultracold bosons in optical lattices are one of the few systems where bosonic matter is known to exhibit strong correlations. Here we push the frontier of our understanding of interacting bosons in optical lattices by adding synthetic…

Quantum Gases · Physics 2018-01-03 Daisuke Yamamoto , I. B. Spielman , C. A. R. Sá de Melo

Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…

Analysis of PDEs · Mathematics 2018-09-18 Claude Bardos , François Golse , Iván Moyano

We present a detailed experimental study of the velocity distribution of atoms cooled in an optical lattice. Our results are supported by full-quantum numerical simulations. Even though the Sisyphus effect, the responsible cooling…

Ultracold polar molecules provide an excellent platform to study quantum many-body spin dynamics, which has become accessible in the recently realized low entropy quantum gas of polar molecules in an optical lattice. To obtain a detailed…

We consider off-equilibrium dynamics at the critical temperature in a class of glassy system. The off-equilibrium correlation and response functions obey a precise scaling form in the aging regime. The structure of the {\it equilibrium}…

Disordered Systems and Neural Networks · Physics 2013-03-18 Francesco Caltagirone , Giorgio Parisi , Tommaso Rizzo

We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body hamiltonian system with long-range interaction showing a second-order phase-transition in the canonical ensemble. Anomalous…

Statistical Mechanics · Physics 2009-10-31 V. Latora , A. Rapisarda , S. Ruffo

We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., a run-and-tumble particle or active Brownian particle etc.), that is confined by an external potential. Focusing on the limit in…

Statistical Mechanics · Physics 2023-08-23 Naftali R. Smith

We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…

Astrophysics · Physics 2015-06-24 D. Syer , S. Tremaine

A fundamental question in many-body physics is how closed quantum systems reach equilibrium. We address this question experimentally and theoretically in an ultracold large-spin Fermi gas where we find a complex interplay between internal…

Atoms trapped in optical lattice have long been a system of interest in the AMO community, and in recent years much study has been devoted to both short- and long-range coherence in this system, as well as to its possible applications to…

Quantum Physics · Physics 2009-11-11 J. F. Kanem , S. Maneshi , S. H. Myrskog , A. M. Steinberg

We consider dynamics of boson condensates in finite optical lattices under a slow external perturbation which brings the system to the unstable equilibrium. It is shown that quantum fluctuations drive the condensate into the maximally…

Statistical Mechanics · Physics 2007-05-23 Anatoli Polkovnikov

We investigate the out-of-equilibrium dynamics of ultracold atoms trapped in an optical lattice and loaded into an optical resonator that is driven transversely. We derive an effective quantum master equation for weak atom-light coupling…

Quantum Gases · Physics 2018-05-22 Ezequiel Rodríguez Chiacchio , Andreas Nunnenkamp

We consider an overdamped Brownian particle subject to an asymptotically flat potential with a trap of depth $U_0$ around the origin. When the temperature is small compared to the trap depth ($\xi=k_B T/U_0 \ll 1$), there exists a range of…

Statistical Mechanics · Physics 2020-10-21 Lucianno Defaveri , Celia Anteneodo , David A. Kessler , Eli Barkai

We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…

Statistical Mechanics · Physics 2026-05-26 Weicheng Fu , Yisen Wang , Yong Zhang , Hong Zhao
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