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

Quantum Thermalization by Stronger Couplings

Haikuan Dong, Shuo Yang, X. F. Liu, C. P. Sun

Published Feb 4, 2007• 0 citations
OpenAlex

Abstract

The role of the system-bath coupling is studied for the generalized canonical thermalization of a system S surrounded by a heat bath B, which was most recently shown [S. Popescu, et al., Nature Physics 2,754(2006) and S. Goldstein et al., Phys. Rev. Lett. 96, 050403(2006)] as a kinematic reduction to a canonical equilibrium state from almost all the pure states of the universe formed by S plus B. This kinematic process is revisited by explicitly considering the energy shell deformation due to the interaction between S and B with an exactly solvable model. By calculating the state numbers of the universe and its subsystems S and B in the deformed energy shells, it is found that, for the overwhelming majority of the universe states (they are entangled at least), the diagonal canonical typicality remains robust with respect to finite interactions between S and B. Particularly, the kinematic decoherence is utilized here to account for the vanishing of the off-diagonal elements of the reduced density matrix of S. It is pointed out that the non-vanishing off-diagonal elements due to the finiteness of bath and the stronger system-bath interaction might offer novelties of the quantum thermalization.

Related papers

Quantum thermalization with couplings

Hang Dong, Shuo Yang, X. F. Liu +1 more

We present an exactly solvable model to study the role of the system-bath coupling for the generalized canonical thermalization, which reduces almost all the pure states of the ``universe'' (formed by a system $S$ plus its surrounding heat bath $B$) to a canonical equilibrium state of $S$. It is found that, for the overwhelming majority of the ``universe'' states (they are entangled at least), the diagonal canonical typicality remains robust with respect to finite interactions between $S$ and $B$. Particularly, a decoherence mechanism is utilized here to account for the vanishing of the off-diagonal elements of the reduced density matrix of $S$. The nonvanishing off-diagonal elements due to the finite size of the bath and the stronger system-bath interaction might offer more to quantum thermalization.

arXiv:quant-ph/0702027•Physical Review A•Oct 23, 2007•29 citations

Origin of the Canonical Ensemble: Thermalization with Decoherence

Shengjun Yuan, Mikhail I. Katsnelson, Hans A. De Raedt

We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced density matrix to a fully decoherent state, and furthermore the diagonal elements of the reduced density matrix approach those expected for the system in the canonical ensemble. We show one exception to the normal case is if the spin system cannot exchange energy with the spin bath. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the canonical ensemble is a state that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics.

arXiv:0904.1501•Journal of the Physical Society of Japan•Aug 28, 2009•32 citations

Canonical Typicality

Sheldon Goldstein, Joel L. Lebowitz, Roderich Tumulka +1 more

It is well known that a system weakly coupled to a heat bath is described by the canonical ensemble when the composite S + B is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true for both classical distributions on the phase space and quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble. This clarifies, expands, and justifies remarks made by Schrödinger in 1952.

arXiv:cond-mat/0511091•Physical Review Letters•Feb 8, 2006•711 citations

Decoherence and Thermalization of Quantum Spin Systems

Shengjun Yuan

In this review, we discuss the decoherence and thermalization of a quantum spin system interacting with a spin bath environment, by numerically solving the time-dependent Schrödinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density matrix approach those expected for the system in the microcanonical or canonical ensemble, depending on the character of the additional integrals of motion. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the microcanonical distribution (in each eigenenergy subspace) and canonical ensemble are states that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics. Furthermore, our numerical results show that a fully decoherent quantum system prefers to stay in an equilibrium state with a maximum entropy, indicating the validity of the second law of thermodynamics in the decoherence process.

arXiv:1005.4776•Journal of Computational and Theoretical Nanoscience•Mar 23, 2011•9 citations

Thermalization from a general canonical principle

Shuai Cui, Cao, Jun-Peng, Hui Jing +2 more

We investigate the time evolution of a generic and finite isolated quantum many-body system starting from a pure quantum state. We find the kinematical general canonical principle proposed by Popescu-Short-Winter for statistical mechanics can be built in a more solid ground by studying the thermalization, i.e. comparing the density matrices themselves rather than the measures of distances. In particular, this allows us to explicitly identify that, from any instantaneous pure state after thermalization, the state of subsystem is like from a microcanonical ensemble or a generalized Gibbs ensemble, but neither a canonical nor a thermal ones due to finite-size effect. Our results are expected to bring the task of characterizing the state after thermalization to completion. In addition, thermalization of coupled systems with different temperatures corresponding to mixed initial states is studied.

arXiv:1110.4690•Oct 21, 2011•1 citation

Strong coupling non-Markovian quantum thermodynamics of a finite-bath system

Devvrat Tiwari, Baibhab Bose, Subhashish Banerjee

The focus is on understanding the quantum thermodynamics of strongly coupled non-Markovian quantum systems. To this end, a non-trivial, non-Markovian model of a central spin surrounded by a spin bath is taken up, and its exact evolution is derived for arbitrary system-bath couplings. The fundamental quantum thermodynamic quantities, such as system and bath internal energies, work, heat, entropy production, and ergotropy, are calculated using the dynamics and the original system (bath) Hamiltonian. An explicit expression for the work, a mismatch between the system and bath internal energies, is derived. The thermodynamic entropy of the system at thermal equilibrium is studied using the Hamiltonian of mean force in the strong coupling regime. The role of a canonical Hamiltonian in calculating the above thermodynamic quantities, a recently developed technique, is also investigated. Furthermore, an interesting observation relevant to the spin bath acting as a charger is made in a scenario where the central spin is envisaged as a quantum battery.

arXiv:2404.15915•The Journal of Chemical Physics•Mar 17, 2025•15 citations
The role of the system-bath coupling is studied for the generalized canonical thermalization of a system S surrounded by a heat bath B, which was most recently shown [S. Popescu, et al., Nature Physics 2,754(2006) and S. Goldstein et al., Phys. Rev. Lett. 96, 050403(2006)] as a kinematic reduction to a canonical equilibrium state from almost all the pure states of the universe formed by S plus B. This kinematic process is revisited by explicitly considering the energy shell deformation due to the interaction between S and B with an exactly solvable model. By calculating the state numbers of the universe and its subsystems S and B in the deformed energy shells, it is found that, for the overwhelming majority of the universe states (they are entangled at least), the diagonal canonical typicality remains robust with respect to finite interactions between S and B. Particularly, the kinematic decoherence is utilized here to account for the vanishing of the off-diagonal elements of the reduced density matrix of S. It is pointed out that the non-vanishing off-diagonal elements due to the finiteness of bath and the stronger system-bath interaction might offer novelties of the quantum thermalization.
We present an exactly solvable model to study the role of the system-bath coupling for the generalized canonical thermalization, which reduces almost all the pure states of the ``universe'' (formed by a system SSS plus its surrounding heat bath BBB) to a canonical equilibrium state of SSS. It is found that, for the overwhelming majority of the ``universe'' states (they are entangled at least), the diagonal canonical typicality remains robust with respect to finite interactions between SSS and BBB. Particularly, a decoherence mechanism is utilized here to account for the vanishing of the off-diagonal elements of the reduced density matrix of SSS. The nonvanishing off-diagonal elements due to the finite size of the bath and the stronger system-bath interaction might offer more to quantum thermalization.
We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced density matrix to a fully decoherent state, and furthermore the diagonal elements of the reduced density matrix approach those expected for the system in the canonical ensemble. We show one exception to the normal case is if the spin system cannot exchange energy with the spin bath. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the canonical ensemble is a state that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics.
It is well known that a system weakly coupled to a heat bath is described by the canonical ensemble when the composite S + B is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true for both classical distributions on the phase space and quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble. This clarifies, expands, and justifies remarks made by Schrödinger in 1952.
In this review, we discuss the decoherence and thermalization of a quantum spin system interacting with a spin bath environment, by numerically solving the time-dependent Schrödinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density matrix approach those expected for the system in the microcanonical or canonical ensemble, depending on the character of the additional integrals of motion. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the microcanonical distribution (in each eigenenergy subspace) and canonical ensemble are states that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics. Furthermore, our numerical results show that a fully decoherent quantum system prefers to stay in an equilibrium state with a maximum entropy, indicating the validity of the second law of thermodynamics in the decoherence process.
We investigate the time evolution of a generic and finite isolated quantum many-body system starting from a pure quantum state. We find the kinematical general canonical principle proposed by Popescu-Short-Winter for statistical mechanics can be built in a more solid ground by studying the thermalization, i.e. comparing the density matrices themselves rather than the measures of distances. In particular, this allows us to explicitly identify that, from any instantaneous pure state after thermalization, the state of subsystem is like from a microcanonical ensemble or a generalized Gibbs ensemble, but neither a canonical nor a thermal ones due to finite-size effect. Our results are expected to bring the task of characterizing the state after thermalization to completion. In addition, thermalization of coupled systems with different temperatures corresponding to mixed initial states is studied.
The focus is on understanding the quantum thermodynamics of strongly coupled non-Markovian quantum systems. To this end, a non-trivial, non-Markovian model of a central spin surrounded by a spin bath is taken up, and its exact evolution is derived for arbitrary system-bath couplings. The fundamental quantum thermodynamic quantities, such as system and bath internal energies, work, heat, entropy production, and ergotropy, are calculated using the dynamics and the original system (bath) Hamiltonian. An explicit expression for the work, a mismatch between the system and bath internal energies, is derived. The thermodynamic entropy of the system at thermal equilibrium is studied using the Hamiltonian of mean force in the strong coupling regime. The role of a canonical Hamiltonian in calculating the above thermodynamic quantities, a recently developed technique, is also investigated. Furthermore, an interesting observation relevant to the spin bath acting as a charger is made in a scenario where the central spin is envisaged as a quantum battery.