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Thermal equilibrium

About: Thermal equilibrium is a research topic. Over the lifetime, 5815 publications have been published within this topic receiving 151634 citations.


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Journal ArticleDOI
TL;DR: In this article, an extended period numerical integration of a baroclinic primitive equation model has been made for the simulation and the study of the dynamics of the atmosphere's general circulation, and the solution corresponding to external gravitational propagation is filtered by requiring the vertically integrated divergence to vanish identically.
Abstract: An extended period numerical integration of a baroclinic primitive equation model has been made for the simulation and the study of the dynamics of the atmosphere's general circulation. The solution corresponding to external gravitational propagation is filtered by requiring the vertically integrated divergence to vanish identically. The vertical structure permits as dependent variables the horizontal wind at two internal levels and a single temperature, with the static stability entering as a parameter. The incoming radiation is a function of latitude only corresponding to the annual mean, and the outgoing radiation is taken to be a function of the local temperature. With the requirement for thermal equilibrium, the domain mean temperature is specified as a parameter. The role of condensation is taken into account only as it effectively reduces the static stability. All other external sources and sinks of heat are assumed to balance each other locally, and are thus omitted. The kinematics are th...

12,952 citations

Journal ArticleDOI
R. H. Dicke1
TL;DR: In this article, the authors considered a radiating gas as a single quantum-mechanical system, and the energy levels corresponding to certain correlations between individual molecules were described, where spontaneous emission of radiation in a transition between two such levels leads to the emission of coherent radiation.
Abstract: By considering a radiating gas as a single quantum-mechanical system, energy levels corresponding to certain correlations between individual molecules are described. Spontaneous emission of radiation in a transition between two such levels leads to the emission of coherent radiation. The discussion is limited first to a gas of dimension small compared with a wavelength. Spontaneous radiation rates and natural line breadths are calculated. For a gas of large extent the effect of photon recoil momentum on coherence is calculated. The effect of a radiation pulse in exciting "super-radiant" states is discussed. The angular correlation between successive photons spontaneously emitted by a gas initially in thermal equilibrium is calculated.

5,672 citations

Journal ArticleDOI
TL;DR: It is shown that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture, and argued that these results constitute a sound foundation for quantum statistical mechanics.
Abstract: We show that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture. Berry's conjecture is expected to hold only if the corresponding classical system is chaotic, and essentially states that the energy eigenfunctions behave as if they were Gaussian random variables. We review the existing evidence, and show that previously neglected effects substantially strengthen the case for Berry's conjecture. We study a rarefied hard-sphere gas as an explicit example of a many-body system which is known to be classically chaotic, and show that an energy eigenstate which obeys Berry's conjecture predicts a Maxwell-Boltzmann, Bose-Einstein, or Fermi-Dirac distribution for the momentum of each constituent particle, depending on whether the wave functions are taken to be nonsymmetric, completely symmetric, or completely antisymmetric functions of the positions of the particles. We call this phenomenon eigenstate thermalization. We show that a generic initial state will approach thermal equilibrium at least as fast as O(\ensuremath{\Elzxh}/\ensuremath{\Delta})${\mathit{t}}^{\mathrm{\ensuremath{-}}1}$, where \ensuremath{\Delta} is the uncertainty in the total energy of the gas. This result holds for an individual initial state; in contrast to the classical theory, no averaging over an ensemble of initial states is needed. We argue that these results constitute a sound foundation for quantum statistical mechanics.

2,649 citations

Journal ArticleDOI
Peter Reimann1
TL;DR: In this paper, the main emphasis is put on directed transport in so-called Brownian motors (ratchets), i.e. a dissipative dynamics in the presence of thermal noise and some prototypical perturbation that drives the system out of equilibrium without introducing a priori an obvious bias into one or the other direction of motion.

2,098 citations

Journal ArticleDOI
13 Apr 2006-Nature
TL;DR: The preparation of out-of-equilibrium arrays of trapped one-dimensional Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions are reported.
Abstract: It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 (87)Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

1,531 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202356
2022118
2021185
2020222
2019215
2018181