Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1608.01469 · Physical review. E

Temperature of a single chaotic eigenstate

F. Borgonovi, Francesco Mattiotti, Felix M. Izrailev

Published Apr 19, 2017• 16 citations
arXivHTMLPDF

Abstract

The onset of thermalization in a closed system of randomly interacting bosons at the level of a single eigenstate is discussed. We focus on the emergence of Bose-Einstein distribution of single-particle occupation numbers, and we give a local criterion for thermalization dependent on the eigenstate energy. We show how to define the temperature of an eigenstate, provided that it has a chaotic structure in the basis defined by the single-particle states. The analytical expression for the eigenstate temperature as a function of both interparticle interaction and energy is complemented by numerical data.

DOI
10.1103/physreve.95.042135

Related papers

Localized thermal states

Fausto Borgonovi, Felix M. Izrailev

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.

arXiv:1709.03258•AIP conference proceedings•Jan 1, 2017•8 citations

Thermalization in a closed quantum system from randomized dynamics

Nikolay V. Gnezdilov, Andrei I. Pavlov

The emergence of statistical mechanics from quantum dynamics is conventionally understood through quantum chaos, the Eigenstate Thermalization Hypothesis (ETH), and canonical typicality, which together explain the thermal behavior of local observables in quantum many-body systems. We provide a distinct mechanism in which, for a quantum many-body system under strong random perturbation, the chaotic behavior of the system's eigenvectors and a constraint on the total energy directly generate a canonical ensemble for the entire system. The canonical ensemble occurs as the first moment of the Porter-Thomas distribution of the system's chaotic eigenstates, and the constraint on the total energy sets the temperature in the ensemble. This yields canonically distributed expectation values without invoking ETH, a microcanonical ensemble, or a subsystem-bath partition for local and global observables. We numerically demonstrate the mechanism for the 1D transverse-field Ising model by showing canonically distributed eigenstate projectors and spin-spin correlators with distinctive temperature dependence of the correlation length. An implementation of this thermalization approach on a quantum computer can be utilized for thermal state preparation.

cond-mat.stat-mechCross-listedarXiv:2601.00056•Jan 2, 2026•0 citations

Dynamical thermalization in Bose-Hubbard systems

Peter Schlagheck, Dima L. Shepelyansky

We numerically study a Bose-Hubbard ring of finite size with disorder containing a finite number of bosons that are subject to an on-site two-body interaction. Our results show that moderate interactions induce dynamical thermalization in this isolated system. In this regime the individual many-body eigenstates are well described by the standard thermal Bose-Einstein distribution for well-defined values of the temperature and the chemical potential, which depend on the eigenstate under consideration. We show that the dynamical thermalization conjecture works well at both positive and negative temperatures. The relations to quantum chaos, quantum ergodicity, and the Åberg criterion are also discussed.

arXiv:1510.01864•Physical review. E•Jan 19, 2016•11 citations

Quantum Chaos and Thermalization for Interacting Particles

Felix M. Izrailev

In this review the problem of statistical description of isolated quantum systems of interacting particles is discussed. Main attention is paid to a recently developed approach which is based on chaotic properties of compound states in the basis of non-interacting particles. In order to demonstrate the most important aspects of this approach, the matrix model of two-body random interaction between Fermi-particles has been used. Different problems have been considered such as the onset of chaos and statistical equilibrium, the relation between the structure of eigenstates and distribution of occupation numbers, the emergence of the Fermi-Dirac distribution in isolated systems of finite number of particles and many others. The application of the approach to dynamical systems with the classical limit is discussed as well.

arXiv:cond-mat/9911297•Nov 19, 1999•3 citations

Time dependence of occupation numbers and thermalization time in closed chaotic many-body systems

V. V. Flambaum, Felix M. Izrailev

We study the time evolution of occupation numbers for interacting Fermi-particles in the situation when exact compound states are "chaotic". This situation is generic for highly excited many-particles states in heavy nuclei, complex atoms, quantum dots, spin systems and quantum computer models. Numerical data show perfect agreement with a simple theory for the onset of thermalization in close systems of interacting particles.

arXiv:quant-ph/0108109•Aug 23, 2001•3 citations

On the onset of thermalization in closed few particles systems: Classical and quantum results

H. Hernández-Saldaña

Abstract A study of quantum-classical correspondence for the onset of thermalization in an isolated system of four interacting particles is presented. Provided that classical dynamics of the system is chaotic, thermalization is present and fits the expected statistical mechanics results. Quantum classical correspondence is established for the classical analogue of the single particle distributions of occupation numbers. The latter quantity is useful to test thermalization and it allows to obtain the microcanonical Boltzmann factor in the quantum and semi-classical cases. The correspondence between them and the statistical mechanics results are surprisingly good considering that we have only four interacting particles. The resulting Boltzmann factor for the occupation number distribution depends on the eigenfunction width, which is a semi-classical parameter explicitly calculated and consistent with the quantum one.

Journal of Physics Conference Series•Jan 1, 2021•0 citations
The onset of thermalization in a closed system of randomly interacting bosons at the level of a single eigenstate is discussed. We focus on the emergence of Bose-Einstein distribution of single-particle occupation numbers, and we give a local criterion for thermalization dependent on the eigenstate energy. We show how to define the temperature of an eigenstate, provided that it has a chaotic structure in the basis defined by the single-particle states. The analytical expression for the eigenstate temperature as a function of both interparticle interaction and energy is complemented by numerical data.
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.
The emergence of statistical mechanics from quantum dynamics is conventionally understood through quantum chaos, the Eigenstate Thermalization Hypothesis (ETH), and canonical typicality, which together explain the thermal behavior of local observables in quantum many-body systems. We provide a distinct mechanism in which, for a quantum many-body system under strong random perturbation, the chaotic behavior of the system's eigenvectors and a constraint on the total energy directly generate a canonical ensemble for the entire system. The canonical ensemble occurs as the first moment of the Porter-Thomas distribution of the system's chaotic eigenstates, and the constraint on the total energy sets the temperature in the ensemble. This yields canonically distributed expectation values without invoking ETH, a microcanonical ensemble, or a subsystem-bath partition for local and global observables. We numerically demonstrate the mechanism for the 1D transverse-field Ising model by showing canonically distributed eigenstate projectors and spin-spin correlators with distinctive temperature dependence of the correlation length. An implementation of this thermalization approach on a quantum computer can be utilized for thermal state preparation.
We numerically study a Bose-Hubbard ring of finite size with disorder containing a finite number of bosons that are subject to an on-site two-body interaction. Our results show that moderate interactions induce dynamical thermalization in this isolated system. In this regime the individual many-body eigenstates are well described by the standard thermal Bose-Einstein distribution for well-defined values of the temperature and the chemical potential, which depend on the eigenstate under consideration. We show that the dynamical thermalization conjecture works well at both positive and negative temperatures. The relations to quantum chaos, quantum ergodicity, and the Åberg criterion are also discussed.
In this review the problem of statistical description of isolated quantum systems of interacting particles is discussed. Main attention is paid to a recently developed approach which is based on chaotic properties of compound states in the basis of non-interacting particles. In order to demonstrate the most important aspects of this approach, the matrix model of two-body random interaction between Fermi-particles has been used. Different problems have been considered such as the onset of chaos and statistical equilibrium, the relation between the structure of eigenstates and distribution of occupation numbers, the emergence of the Fermi-Dirac distribution in isolated systems of finite number of particles and many others. The application of the approach to dynamical systems with the classical limit is discussed as well.
Abstract A study of quantum-classical correspondence for the onset of thermalization in an isolated system of four interacting particles is presented. Provided that classical dynamics of the system is chaotic, thermalization is present and fits the expected statistical mechanics results. Quantum classical correspondence is established for the classical analogue of the single particle distributions of occupation numbers. The latter quantity is useful to test thermalization and it allows to obtain the microcanonical Boltzmann factor in the quantum and semi-classical cases. The correspondence between them and the statistical mechanics results are surprisingly good considering that we have only four interacting particles. The resulting Boltzmann factor for the occupation number distribution depends on the eigenfunction width, which is a semi-classical parameter explicitly calculated and consistent with the quantum one.