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arXiv:0807.2418 · Physical Review E

Damped bounces of an isolated perfect quantum gas

S. Camalet

Published Dec 12, 2008• 1 citation
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Abstract

The issue of the thermalization of an isolated quantum system is addressed by considering a perfect gas confined by gravity and initially trapped above a certain height. As we are interested in the behavior of truly isolated systems, we assume the gas is in a pure state of macroscopically well-defined energy. We show that, in general, for single-particle distributions, such a state is strictly equivalent to the microcanonical mixed state at the same energy. We derive an expression for the time-dependent gas density that depends on the initial gas state only via a few thermodynamic parameters. Though we consider noninteracting particles, the density relaxes into an asymptotic profile, but it is not the thermal equilibrium one determined by the gas energy and particle number.

DOI
10.1103/physreve.78.061112

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The issue of the thermalization of an isolated quantum system is addressed by considering a perfect gas confined by gravity and initially trapped above a certain height. As we are interested in the behavior of truly isolated systems, we assume the gas is in a pure state of macroscopically well-defined energy. We show that, in general, for single-particle distributions, such a state is strictly equivalent to the microcanonical mixed state at the same energy. We derive an expression for the time-dependent gas density that depends on the initial gas state only via a few thermodynamic parameters. Though we consider noninteracting particles, the density relaxes into an asymptotic profile, but it is not the thermal equilibrium one determined by the gas energy and particle number.
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Abstract Motivated by current interest in the dynamics of trapped quantum gases, we study the microcanonical dynamics of a trapped 1D gas of classical particles interacting via a finite-range repulsive force of tunable strength. We examine two questions whose analogues have been of interest in quantum dynamics: (1) the breathing mode (size oscillation) dynamics of the trapped gas and the dependence of the breathing frequency on the interaction strength, and (2) the long-time relaxation and possible thermalization of the finite isolated gas. We show that the breathing mode frequency has non-monotonic dependence on the magnitude of the mutual repulsion, decreasing for small interactions and increasing for larger interactions. We explain these dependences in terms of slowing-down or speeding-up effects of two-body collision processes. We find that the gas thermalizes within a reasonable finite timescale in the sense of single-particle energies acquiring a Boltzmann distribution, only when the interaction strength is large compared to the energy per particle.
Motivated by current interest in the dynamics of trapped quantum gases, we study the microcanonical dynamics of a trapped 1D gas of classical particles interacting via a finite-range repulsive force of tunable strength. We examine two questions whose analogues have been of interest in quantum dynamics: (1) the breathing mode (size oscillation) dynamics of the trapped gas and the dependence of the breathing frequency on the interaction strength, and (2) the long-time relaxation and possible thermalization of the finite isolated gas. We show that the breathing mode frequency has non-monotonic dependence on the magnitude of the mutual repulsion, decreasing for small interactions and increasing for larger interactions. We explain these dependences in terms of slowing-down or speeding-up effects of two-body collision processes. We find that the gas thermalizes within a reasonable finite timescale in the sense of single-particle energies acquiring a Boltzmann distribution, only when the interaction strength is large compared to the energy per particle.
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We consider isolated many-body quantum systems which do not thermalize; i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A general analytical theory is worked out for the typical temporal relaxation behavior in such cases. The main prerequisites are initial conditions which appreciably populate many energy levels and do not give rise to significant spatial inhomogeneities on macroscopic scales. The theory explains very well the experimental and numerical findings in a trapped-ion quantum simulator exhibiting many-body localization, in ultracold atomic gases, and in integrable hard-core boson and XXZ models.
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