Temperature of a single chaotic eigenstate

Borgonovi, Fausto; Mattiotti, Francesco; Izrailev, F. M.

doi:10.1103/physreve.95.042135

Cited by 15 publications

(33 citation statements)

References 49 publications

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“…This energy is higher by some amount ∆ α than the eigenvalue E α , in the region where the density of states increases, see Ref. [18]. Correspondingly, the effective temperature T dres is higher than that obtained with E α .…”

Section: Single-particle Occupation Numbersmentioning

confidence: 86%

Localized thermal states

Borgonovi

Izrailev

2017

AIP Conference Proceedings

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Abstract. It is believed that thermalization in closed systems of interacting particles can occur only when the eigenstates are fully delocalized and chaotic in the preferential (unperturbed) basis of the total Hamiltonian. Here we demonstrate that at variance with this common belief the typical situation in the systems with two-body inter-particle interaction is much more complicated and allows to treat as thermal even eigenstates that are not fully delocalized. Using a semi-analytical approach we establish the conditions for the emergence of such thermal states in a model of randomly interacting bosons. Our numerical data show an excellent correspondence with the predicted properties of localized thermal eigenstates.

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Section: Single-particle Occupation Numbersmentioning

confidence: 86%

Localized thermal states

Borgonovi

Izrailev

2017

AIP Conference Proceedings

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“…To date it is understood that the validity of statistical mechanics can be justified not only by averaging over a number of eigenstates with close energies, but also with the use of a single eigenstate if the latter consists of many uncorrelated components in the physically chosen basis. Specifically, it was shown that BE and FD distributions emerge also on the level of individual eigenstates if they are strongly chaotic [8,10,11]. The most intriguing point here is that both distributions appear even if the number of particles is small; this happens due to the fast growth of the number of components in many-body eigenstates in dependence on the number of particles.…”

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confidence: 80%

“…One of the basic statistical properties of many-body systems is either the Bose-Einstein (BE) or Fermi-Dirac (FD) distribution that emerge in the thermodynamic limit due to the combinatorics and without inter-particle interaction. As for finite isolated systems, the mechanism for the onset of BE and FD distributions is the chaotic structure of many-body eigenstates [3,5,[7][8][9][10]. In this case, the interaction between particles plays a crucial role: the fewer the particles the stronger the inter-particle interaction has to be for the emergence of the statistical properties.…”

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confidence: 99%

Emergence of correlations in the process of thermalization of interacting bosons

Borgonovi

Izrailev

2019

Phys. Rev. E

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We address the question of the relevance of thermalization to the increase of correlations in the quench dynamics of an isolated system with a finite number of interacting bosons. Specifically, we study how, in the process of thermalization, the correlations between occupation numbers increase in time resulting in the emergence of the Bose-Einstein distribution. We show, both analytically and numerically, that before saturation the two-point correlation function increases quadratically in time. This time dependence is at variance with the exponential increase of the number of principal components of the wave function, recently discovered and explained in Ref. [1]. We also demonstrate that the out-of-time-order correlator (OTOC) increases algebraically in time but not exponentially as predicted in many publications. Our results, that can be confirmed experimentally in traps with interacting bosons, may be also relevant to the problem of black hole scrambling. arXiv:1806.00435v1 [cond-mat.stat-mech] 1 Jun 2018

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“…Notwithstanding this, the ingredients indispensable for this emergence remain an open problem. It has been shown that the direct interaction between particles, via driving many-body quantum chaos, gives rise to complex structures of eigenstates, from which the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions arise [3,10,13,14]. The need of this interaction conforms to standard statistical mechanics [15].…”

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confidence: 94%

Hidden thermal structure in Fock space

et al. 2018

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The emergence of quantum statistical mechanics from individual pure states of closed manybody systems is currently under intensive investigations. While most efforts have been put on the impacts of the direct interaction (i.e., the usual mutual interaction) between particles, here we study systematically and analytically the impacts of the exchange interaction, that arises from the particle indistinguishability. We show that this interaction leads an overwhelming number of Fock states to exhibit a structure, that can be resolved only by observables adjusted according to system's dynamical properties and from which thermal distributions emerge. This hidden thermal structure in Fock space is found to be related to the so-called limit shape of random geometric objects in mathematics. The structure enables us to uncover, for both ideal and nonideal Fermi gases, new mechanisms for the emergence of quantum statistical mechanics from individual eigenstates.

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Temperature of a single chaotic eigenstate

Cited by 15 publications

References 49 publications

Localized thermal states

Localized thermal states

Emergence of correlations in the process of thermalization of interacting bosons

Hidden thermal structure in Fock space

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