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:1903.12083 · Physical Review A

Threshold coupling strength for equilibration between small systems

Ralf Bürkle, J. R. Anglin

Published Jun 19, 2019• 4 citations
arXivHTMLPDF

Abstract

In this paper we study the thermal equilibration of small bipartite Bose-Hubbard systems, both quantum mechanically and in mean-field approximation. In particular we consider small systems composed of a single-mode ``thermometer'' coupled to a three-mode ``bath,'' with no additional environment acting on the four-mode system, and test the hypothesis that the thermometer will thermalize if and only if the bath is chaotic. We find that chaos in the bath alone is neither necessary nor sufficient for equilibration in these isolated four-mode systems. The two subsystems can thermalize if the combined system is chaotic even when neither subsystem is chaotic in isolation, and under full quantum dynamics there is a minimum coupling strength between the thermometer and the bath below which the system does not thermalize even if the bath itself is chaotic. We show that the quantum coupling threshold scales like $1/N$ (where $N$ is the total particle number), so that the classical results are obtained in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$.

DOI
10.1103/physreva.99.063617

Related papers

Quantum coherence controls the nature of equilibration and thermalization in coupled chaotic systems

Jethin J. Pulikkottil, Arul Lakshminarayan, Shashi C. L. Srivastava +3 more

A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax toward an equilibrium. It is found that quantum coherence of the initial product states in the energy eigenbasis of the subsystems-quantified by the off-diagonal elements of the subsystem density matrices-can be viewed as a resource for equilibration and thermalization as manifested by the entanglement generated. Results are given for four distinct perturbation strength regimes, the ultraweak, weak, intermediate, and strong regimes. For each, three types of tensor product states are considered for the initial state: uniform superpositions, random superpositions, and individual subsystem eigenstates. A universal timescale is identified involving the interaction strength parameter. In particular, maximally coherent initial product states (a form of uniform superpositions) thermalize under time evolution for any perturbation strength in spite of the fact that in the ultraweak perturbative regime the underlying eigenstates of the system have a tensor product structure and are not at all thermal-like; though the time taken to thermalize tends to infinity as the interaction vanishes. Moreover, it is shown that in the ultraweak regime the initial entanglement growth of the system whose initial states are maximally coherent is quadratic-in-time, in contrast to the widely observed linear behavior.

arXiv:2204.07561•Physical review. E•Feb 15, 2023•11 citations

Probing quantum thermalization and localization in Bose-Hubbard systems

Antonio Rubio-Abadal

The experimental control and observation of quantum many-body systems has become a reality with the advent of ultracold quantum matter. The high level of isolation of these experiments, together with the development of novel measurement techniques, has revived a fundamental debate concerning the thermal equilibration of isolated quantum systems, commonly named "quantum thermalization". In this thesis we make use of a quantum-gas microscope to explore the thermalizing dynamics of highly isolated systems of ultracold bosonic atoms in optical lattices. The ability to prepare and control quantum systems made up of hundreds of atoms makes it possible to explore regimes that represent a challenge for classical numeric simulations. A major part of this dissertation deals with Bose-Hubbard systems in the presence of quenched disorder. We begin by studying the microscopic properties of its phases near equilibrium, where by tuning the strength of the disorder, observe features consistent with the emergence of a so-called Bose-glass phase. We then continue by preparing states far from equilibrium and exploring their quantum many-body dynamics. In particular, we observe signatures of the phenomenon of "many-body localization", which implies a breakdown of quantum thermalization. In addition, we study whether localized systems can be thermalized via the coupling to a bath of few degrees of freedom, i.e. a quantum bath. We do so by preparing a mixture of two interacting atomic species, where one acts as the bath and the other as the localized system. We do observe delocalizing dynamics for large enough baths, though in regimes of weak coupling localization can survive for extremely long times. The second main topic of this thesis is the thermalization of periodically driven many-body systems, so-called Floquet thermalization. In these systems, the absence of energy conservation eventually brings any initial state into a featureless infinite-temperature one. However, for sufficiently high frequencies this thermalization process can take arbitrarily long times, which can enable the engineering of exotic long-lived prethermal states. We use the high isolation of our system, together with the high sensitivity of quantum-gas microscopy, to measure the heating rates for a range of driving frequencies and interaction regimes. Our results show a dramatic suppression of the heating as the frequency of the drive is increased, which is consistent with theoretical expectations.

•Jan 1, 2020•0 citations

Thermalization of small quantum systems: from the zeroth law of thermodynamics

Jiaozi Wang, Wen-ge Wang, Jiao Wang

Abstract Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have been achieved. Here, we study thermalization of small quantum systems that interact with large chaotic environments under the consideration of Schrödinger evolution of composite systems, from the perspective of the zeroth law of thermodynamics. Namely, we consider a small quantum system that is brought into contact with a large environmental system; after they have relaxed, they are separated and their temperatures are studied. Our question is under what conditions the small system may have a detectable temperature that is identical with the environmental temperature. This should be a necessary condition for the small quantum system to be thermalized and to have a well-defined temperature. By using a two-level probe quantum system that plays the role of a thermometer, we find that the zeroth law is applicable to quantum chaotic systems, but not to integrable systems.

arXiv:1905.06100•Journal of Physics A Mathematical and Theoretical•Dec 21, 2021•1 citation

Thermalization in the two-body random ensemble

V K B Kota, A Relaño, J. Retamosa +1 more

Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems.These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and especially the dynamical transition from integrability to chaos.By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, such as the energy and structure of the initial state, or the dimension of the Hilbert space.We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originating at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable.As the strength of the residual interaction is increased, an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems.When all the signatures of chaos are fulfilled, including the quasicomplete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators.Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.

arXiv:1102.0528•Journal of Statistical Mechanics Theory and Experiment•Oct 31, 2011•25 citations

Quantum dynamics of a four-well Bose-Hubbard model with two different tunneling rates

C.V. Chianca, M. K. Olsen

We consider a theoretical model of a four-mode Bose-Hubbard model consisting of two pairs of wells coupled via two processes with two different rates. The model is naturally divided into two subsystems with strong intrasystem coupling and much weaker coupling between the two subsystems and has previously been introduced as a model for Josephson heat oscillations by Strzys and Anglin [Phys. Rev. A 81, 043616 (2010)]. We examine the quantum dynamics of this model for a range of different initial conditions, in terms of both the number distribution among the wells and the quantum statistics. We find that the time evolution is different to that predicted by a mean-field model and that this system exhibits a wide range of interesting behaviours. We find that the system equilibrates to a maximum entropy state and is thus a useful model for quantum thermalisation. As our model may be realized to a good approximation in the laboratory, it becomes a candidate for experimental investigation.

arXiv:1101.0451•Physical Review A•Apr 8, 2011•27 citations

Thermalization of local observables in small Hubbard lattices

Sam Genway, A. F. Ho, Derek K. K. Lee

We present a study of thermalization of a small isolated Hubbard lattice cluster prepared in a pure state with a well-defined energy. We examine how a two-site subsystem of the lattice thermalizes with the rest of the system as its environment. We explore numerically the existence of thermalization over a range of system parameters, such as the interaction strength, system size, and the strength of the coupling between the subsystem and the rest of the lattice. We find thermalization over a wide range of parameters and that interactions are crucial for efficient thermalization of small systems. We relate this thermalization behavior to the eigenstate thermalization hypothesis and quantify numerically the extent to which eigenstate thermalization holds. We also verify our numerical results theoretically with the help of previously established results from random matrix theory for the local density of states, particularly the finite-size scaling for the onset of thermalization.

arXiv:1204.3036•Physical Review A•Aug 9, 2012•49 citations
In this paper we study the thermal equilibration of small bipartite Bose-Hubbard systems, both quantum mechanically and in mean-field approximation. In particular we consider small systems composed of a single-mode thermometer'' coupled to a three-mode bath,'' with no additional environment acting on the four-mode system, and test the hypothesis that the thermometer will thermalize if and only if the bath is chaotic. We find that chaos in the bath alone is neither necessary nor sufficient for equilibration in these isolated four-mode systems. The two subsystems can thermalize if the combined system is chaotic even when neither subsystem is chaotic in isolation, and under full quantum dynamics there is a minimum coupling strength between the thermometer and the bath below which the system does not thermalize even if the bath itself is chaotic. We show that the quantum coupling threshold scales like 1/N1/N1/N (where NNN is the total particle number), so that the classical results are obtained in the limit N\ensuremath→\ensuremath∞N\ensuremath{\rightarrow}\ensuremath{\infty}N\ensuremath→\ensuremath∞.
A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax toward an equilibrium. It is found that quantum coherence of the initial product states in the energy eigenbasis of the subsystems-quantified by the off-diagonal elements of the subsystem density matrices-can be viewed as a resource for equilibration and thermalization as manifested by the entanglement generated. Results are given for four distinct perturbation strength regimes, the ultraweak, weak, intermediate, and strong regimes. For each, three types of tensor product states are considered for the initial state: uniform superpositions, random superpositions, and individual subsystem eigenstates. A universal timescale is identified involving the interaction strength parameter. In particular, maximally coherent initial product states (a form of uniform superpositions) thermalize under time evolution for any perturbation strength in spite of the fact that in the ultraweak perturbative regime the underlying eigenstates of the system have a tensor product structure and are not at all thermal-like; though the time taken to thermalize tends to infinity as the interaction vanishes. Moreover, it is shown that in the ultraweak regime the initial entanglement growth of the system whose initial states are maximally coherent is quadratic-in-time, in contrast to the widely observed linear behavior.
The experimental control and observation of quantum many-body systems has become a reality with the advent of ultracold quantum matter. The high level of isolation of these experiments, together with the development of novel measurement techniques, has revived a fundamental debate concerning the thermal equilibration of isolated quantum systems, commonly named "quantum thermalization". In this thesis we make use of a quantum-gas microscope to explore the thermalizing dynamics of highly isolated systems of ultracold bosonic atoms in optical lattices. The ability to prepare and control quantum systems made up of hundreds of atoms makes it possible to explore regimes that represent a challenge for classical numeric simulations. A major part of this dissertation deals with Bose-Hubbard systems in the presence of quenched disorder. We begin by studying the microscopic properties of its phases near equilibrium, where by tuning the strength of the disorder, observe features consistent with the emergence of a so-called Bose-glass phase. We then continue by preparing states far from equilibrium and exploring their quantum many-body dynamics. In particular, we observe signatures of the phenomenon of "many-body localization", which implies a breakdown of quantum thermalization. In addition, we study whether localized systems can be thermalized via the coupling to a bath of few degrees of freedom, i.e. a quantum bath. We do so by preparing a mixture of two interacting atomic species, where one acts as the bath and the other as the localized system. We do observe delocalizing dynamics for large enough baths, though in regimes of weak coupling localization can survive for extremely long times. The second main topic of this thesis is the thermalization of periodically driven many-body systems, so-called Floquet thermalization. In these systems, the absence of energy conservation eventually brings any initial state into a featureless infinite-temperature one. However, for sufficiently high frequencies this thermalization process can take arbitrarily long times, which can enable the engineering of exotic long-lived prethermal states. We use the high isolation of our system, together with the high sensitivity of quantum-gas microscopy, to measure the heating rates for a range of driving frequencies and interaction regimes. Our results show a dramatic suppression of the heating as the frequency of the drive is increased, which is consistent with theoretical expectations.
Abstract Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have been achieved. Here, we study thermalization of small quantum systems that interact with large chaotic environments under the consideration of Schrödinger evolution of composite systems, from the perspective of the zeroth law of thermodynamics. Namely, we consider a small quantum system that is brought into contact with a large environmental system; after they have relaxed, they are separated and their temperatures are studied. Our question is under what conditions the small system may have a detectable temperature that is identical with the environmental temperature. This should be a necessary condition for the small quantum system to be thermalized and to have a well-defined temperature. By using a two-level probe quantum system that plays the role of a thermometer, we find that the zeroth law is applicable to quantum chaotic systems, but not to integrable systems.
Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems.These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and especially the dynamical transition from integrability to chaos.By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, such as the energy and structure of the initial state, or the dimension of the Hilbert space.We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originating at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable.As the strength of the residual interaction is increased, an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems.When all the signatures of chaos are fulfilled, including the quasicomplete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators.Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.
We consider a theoretical model of a four-mode Bose-Hubbard model consisting of two pairs of wells coupled via two processes with two different rates. The model is naturally divided into two subsystems with strong intrasystem coupling and much weaker coupling between the two subsystems and has previously been introduced as a model for Josephson heat oscillations by Strzys and Anglin [Phys. Rev. A 81, 043616 (2010)]. We examine the quantum dynamics of this model for a range of different initial conditions, in terms of both the number distribution among the wells and the quantum statistics. We find that the time evolution is different to that predicted by a mean-field model and that this system exhibits a wide range of interesting behaviours. We find that the system equilibrates to a maximum entropy state and is thus a useful model for quantum thermalisation. As our model may be realized to a good approximation in the laboratory, it becomes a candidate for experimental investigation.
We present a study of thermalization of a small isolated Hubbard lattice cluster prepared in a pure state with a well-defined energy. We examine how a two-site subsystem of the lattice thermalizes with the rest of the system as its environment. We explore numerically the existence of thermalization over a range of system parameters, such as the interaction strength, system size, and the strength of the coupling between the subsystem and the rest of the lattice. We find thermalization over a wide range of parameters and that interactions are crucial for efficient thermalization of small systems. We relate this thermalization behavior to the eigenstate thermalization hypothesis and quantify numerically the extent to which eigenstate thermalization holds. We also verify our numerical results theoretically with the help of previously established results from random matrix theory for the local density of states, particularly the finite-size scaling for the onset of thermalization.