Finite quantum environments as thermostats: an analysis based on the Hilbert space average method

Gemmer, Jochen; Michel, M.

doi:10.1140/epjb/e2006-00407-3

Cited by 42 publications

(59 citation statements)

References 20 publications

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“…(10) and (11)], ðt=Þ and ðt=Þ [see eqs. (12) and (13)] for the case that there is a fairly strong coupling between the system S and the environment E (jÁ=Jj ¼ 0:4) and for different values of the initial temperature of the environment. From Fig.…”

Section: Resultsmentioning

confidence: 99%

Approach to Equilibrium in Nano-scale Systems at Finite Temperature

et al. 2010

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We study the time evolution of the reduced density matrix of a system of spin-1/2 particles interacting with an environment of spin-1/2 particles. The initial state of the composite system is taken to be a product state of a pure state of the system and a pure state of the environment. The latter pure state is prepared such that it represents the environment at a given finite temperature in the canonical ensemble. The state of the composite system evolves according to the time-dependent Schrödinger equation, the interaction creating entanglement between the system and the environment. It is shown that independent of the strength of the interaction and the initial temperature of the environment, all the eigenvalues of the reduced density matrix converge to their stationary values, implying that also the entropy of the system relaxes to a stationary value. We demonstrate that the difference between the canonical density matrix and the reduced density matrix in the stationary state increases as the initial temperature of the environment decreases. As our numerical simulations are necessarily restricted to a modest number of spin-1/2 particles (<36), but do not rely on time-averaging of observables nor on the assumption that the coupling between system and environment is weak, they suggest that the stationary state of the system directly follows from the time evolution of a pure state of the composite system, even if the size of the latter cannot be regarded as being close to the thermodynamic limit.

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Section: Resultsmentioning

confidence: 99%

Approach to Equilibrium in Nano-scale Systems at Finite Temperature

et al. 2010

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“…In many problems the thermal bath can be highly structured, containing a finite number of modes, which strongly influence back the system dynamics. In fact, the system may be driven towards equilibrium through increasing correlations with the bath [27][28][29][30][31][32][33][34], in contrast with situations in which system and bath remain uncorrelated [35]. Such a complex phenomenon was also observed for the energy transfer between a light-harvesting protein and a reaction center protein [36,37].…”

Section: Introductionmentioning

confidence: 95%

Monogamy and backflow of mutual information in non-Markovian thermal baths

2014

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We investigate the dynamics of information among the parties of tripartite systems. We start by proving two results concerning the monogamy of mutual information. The first one states that mutual information is monogamous for generic tripartite pure states. The second shows that, in general, mutual information is monogamous only if the amount of genuine tripartite correlations is large enough. Then, we analyze the internal dynamics of tripartite systems whose parties do not exchange energy. In particular, we allow for one of the subsystems to play the role of a finite thermal bath. As a result, we find a typical scenario in which local information tends to be converted into delocalized information. Moreover, we show that (i) the information flow is reversible for finite thermal baths at low temperatures, (ii) monogamy of mutual information is respected throughout the dynamics, and (iii) genuine tripartite correlations are typically present. Finally, we analytically calculate a quantity capable of revealing favorable regimes for non-Markovianity in our model.

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“…Quantum many-body systems in strict isolation have experienced an upsurge of interest in recent years, also due to the advent of cold atomic gases [10], the discovery of many-body localized phases [11], and the invention of powerful numerical techniques such as density matrix renormalization group [2]. In particular, understanding the existence of equilibration and thermalization has seen substantial progress [12,13] by as fascinating concepts as eigenstate thermalization [14][15][16] and typicality of pure states [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. However, much less is known on the route to equilibrium as such [31,32].…”

Section: Introductionmentioning

confidence: 99%

Relation between far-from-equilibrium dynamics and equilibrium correlation functions for binary operators

Richter

Steinigeweg

2019

Phys. Rev. E

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Linear response theory (LRT) is one of the main approaches to the dynamics of quantum manybody systems. However, this approach has limitations and requires, e.g., that the initial state is (i) mixed and (ii) close to equilibrium. In this paper, we discuss these limitations and study the nonequilibrium dynamics for a certain class of properly prepared initial states. Specifically, we consider thermal states of the quantum system in the presence of an additional static force which, however, become nonequilibrium states when this static force is eventually removed. While for weak forces the relaxation dynamics is well captured by LRT, much less is known in the case of strong forces, i.e., initial states far away from equilibrium. Summarizing our main results, we unveil that, for high temperatures, the nonequilibrium dynamics of so-called binary operators is always generated by an equilibrium correlation function. In particular, this statement holds true for states in the far-from-equilibrium limit, i.e., outside the linear response regime. In addition, we confirm our analytical results by numerically studying the dynamics of local fermionic occupation numbers and local energy densities in the spin-1/2 Heisenberg chain. Remarkably, these simulations also provide evidence that our results qualitatively apply in a more general setting, e.g., in the anisotropic XXZ model where the local energy is a non-binary operator, as well as for a wider range of temperature. Furthermore, exploiting the concept of quantum typicality, all of our findings are not restricted to mixed states, but are valid for pure initial states as well.

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Finite quantum environments as thermostats: an analysis based on the Hilbert space average method

Cited by 42 publications

References 20 publications

Approach to Equilibrium in Nano-scale Systems at Finite Temperature

Approach to Equilibrium in Nano-scale Systems at Finite Temperature

Monogamy and backflow of mutual information in non-Markovian thermal baths

Relation between far-from-equilibrium dynamics and equilibrium correlation functions for binary operators

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