A numerical verification of the prediction of an exponential velocity spectrum for a gas of particles in a time-dependent potential well

Błocki, J.; Brut, F.; Świa̧tecki, W.J.

doi:10.1016/0375-9474(93)90360-a

Cited by 13 publications

(11 citation statements)

References 2 publications

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“…Its derivation is based on the chaotic adiabatic dynamics [7][8][9][10] in which the distinction is being made between fast (single-particle) and slow (collective) degrees of freedom and the damping of collective motion results from the coupling to the fast modes. In the classical domain, the range of validity of the wall fomula for sufficiently chaotic systems seems to extend beyond the adiabaticity constraint, as shown by numerical studies [11]. Similar conclusion follows from studies of quantum systems [1,2], in which, however, only one oscillation period was investigated.…”

Section: Introductionmentioning

confidence: 52%

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Excitation of a quantum gas of independent particles under periodic perturbation in integrable or nonintegrable potentials

Magierski

Skalski²,

Błocki

1997

Phys. Rev. C

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The excitation of a quantum gas of 112 independent fermions in the timedependent potential well, periodically oscillating around the spherical shape, was followed over 10 oscillation cycles. Five different oscillation frequencies are considered for each of the five types of deformations: spheroidal and Legendre polynomial ripples: P 3 , P 4 , P 5 and P 6 . The excitation rate of the gas in the deforming hard-walled cavities substantially decreases after initial one or two cycles and the final excitation energy is a few times smaller than the wall formula predictions. Qualitatively similar results are obtained for the diffused Woods-Saxon well. The details and possible origins of this behaviour are discussed as well as the consequences for the one-body dissipation model of nuclear dynamics.

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Section: Introductionmentioning

confidence: 52%

“…The first effect is known from classical calculations [11] and was related to the integrability of motion in the spheroidal well. Since it was discussed in previous papers we make here only few comments.…”

Section: Discussionmentioning

confidence: 99%

Excitation of a quantum gas of independent particles under periodic perturbation in integrable or nonintegrable potentials

Magierski

Skalski²,

Błocki

1997

Phys. Rev. C

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“…6.9, as shown in Ref. [14], and supported by numerical simulations [15], is that, asymptotically with time, a chaotic adial:>atic billiard gas will achieve a distribution of particle velocities which has a universal form: …”

Section: =I De Tj(e T) Ementioning

confidence: 59%

Energy diffusion in a chaotic adiabatic billiard gas

Jarzynski

1993

Phys. Rev. E

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“…If this is the case, then one can consider a continuous driving protocol instead of repeated quenches and all the results will be the same. Such a setup was analyzed by Jarzynski [213] followed by other works [193,[220][221][222][223][224]]. An interesting and nontrivial result that emerges from this analysis is a nonequilibrium exponential velocity distribution (to be contrasted with the Gaussian Maxwell distribution).…”

Section: Heating a Particle In A Fluctuating Chaotic Cavitymentioning

confidence: 99%

From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics

D’Alessio

Kafri

Polkovnikov

et al. 2016

Advances in Physics

2,144

2,527

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This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory. To this end, we present a brief overview of classical and quantum chaos, as well as random matrix theory and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the implications of quantum chaos and ETH to thermodynamics. Basic thermodynamic relations are derived, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, the fluctuation-dissipation relation, and the Einstein and Onsager relations. In particular, it is shown that quantum chaos allows one to prove these relations for individual Hamiltonian eigenstates and thus extend them to arbitrary stationary statistical ensembles. In some cases, it is possible to extend their regimes of applicability beyond the standard thermal equilibrium domain. We then show how one can use these relations to obtain nontrivial universal energy distributions in continuously driven systems. At the end of the review, we briefly discuss the relaxation dynamics and description after relaxation of integrable quantum systems, for which ETH is violated. We present results from numerical experiments and analytical studies of quantum quenches at integrability. We introduce the concept of the generalized Gibbs ensemble, and discuss its connection with ideas of prethermalization in weakly interacting systems.

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A numerical verification of the prediction of an exponential velocity spectrum for a gas of particles in a time-dependent potential well

Cited by 13 publications

References 2 publications

Excitation of a quantum gas of independent particles under periodic perturbation in integrable or nonintegrable potentials

Excitation of a quantum gas of independent particles under periodic perturbation in integrable or nonintegrable potentials

Energy diffusion in a chaotic adiabatic billiard gas

From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics

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