Finite quantum dissipation: the challenge of obtaining specific heat

Hänggi, Peter; Ingold, Gert‐Ludwig; Talkner, Peter

doi:10.1088/1367-2630/10/11/115008

Cited by 131 publications

(253 citation statements)

References 17 publications

(40 reference statements)

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“…the free particle result in which the friction coefficient γ appears in the denominator, in agreement to the corresponding result given in [21], after a proper counting of the degree of freedom.…”

Section: Heat Capacitysupporting

confidence: 89%

Dissipative quantum systems and the heat capacity

et al. 2010

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We present a detailed study of the quantum dissipative dynamics of a charged particle in a magnetic field. Our focus of attention is the effect of dissipation on the low-and high-temperature behavior of the specific heat at constant volume. After providing a brief overview of two distinct approaches to the statistical mechanics of dissipative quantum systems, viz., the ensemble approach of Gibbs and the quantum Brownian motion approach due to Einstein, we present exact analyses of the specific heat. While the low-temperature expressions for the specific heat, based on the two approaches, are in conformity with power-law temperature-dependence, predicted by the third law of thermodynamics, and the high-temperature expressions are in agreement with the classical equipartition theorem, there are surprising differences between the dependencies of the specific heat on different parameters in the theory, when calculations are done from these two distinct methods. In particular, we find puzzling influences of boundary-confinement and the bath-induced spectral cutoff frequency. Further, when it comes to the issue of approach to equilibrium, based on the Einstein method, the way the asymptotic limit (t → ∞) is taken, seems to assume significance.

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Section: Heat Capacitysupporting

confidence: 89%

Dissipative quantum systems and the heat capacity

et al. 2010

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“…Now, we specify the exact content of the condition (iv) discussed below Eq. (8), that is, we assume that the width δE is fixed, or decreases sufficiently slowly with increasing size of the environment, such that δe/δE goes to zero in the large-environment limit. As shown in Appendix C, under this condition, ρ S δE has properties similar to those of ρ S d discussed above in P2, hence, has the usual canonical form.…”

Section: A the Case Of Quite Weak Interactionmentioning

confidence: 99%

“…Recently, development of technologies has made it possible to perform direct experimental studies on thermalization of systems of the mesoscopic, even microscopic scale [1,2], showing deviation from the standard canonical distribution due to non-weak interaction [1]. Meanwhile, theoretical studies and numerical simulations have been also carried out, some showing approach to ordinary thermal states [3,4], while some suggesting significant deviations in certain cases [5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Statistical description of small quantum systems beyond the weak-coupling limit

Wang¹

2012

Phys. Rev. E

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An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is given by a renormalized self-Hamiltonian of the studied system, which appropriately takes into account the influence of the system-environment interaction. In the case that the system has a narrow spectrum and the environment is sufficiently large, the modification to the self-Hamiltonian usually has a mean-field feature, given by an environmental average of the interaction Hamiltonian. In other cases, the modification may be beyond the meanfield approximation.

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“…Note that the thermodynamics that follows from the partition function Z S ðtÞ comprises the equilibrium properties of the open quantum system in a consistent manner including the influence of environment and coupling [11,12,[18][19][20][21]: In particular, the thermodynamic functions that follow from this thermodynamic partition function do not violate any known thermodynamic law.…”

Section: Selected For a Viewpoint In Physics P H Y S I C A L R E V I mentioning

confidence: 99%

“…(1) and (2) to the case of weak coupling is consistent with the construction of quantum and classical statistical mechanics which relies on that assumption. In striking contrast, extending the methods of statistical mechanics to cases that involve a nonnegligible system-environment interaction presents a major challenge [11,12]. Addressing this question is by now becoming more and more pressing, as the advancement of technology poses us in the position to investigate experimentally the thermodynamic behavior of nanosystems operating in the quantum regime, whose reduced sizes make the system-environment coupling an important issue.…”

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confidence: 99%

Fluctuations in open systems

Ritort¹

2009

Physics

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Based on the observation that the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment is the difference between the free energy of the total system and that of the bare environment, the validity of the Crooks theorem and of the Jarzynski equality is extended to open quantum systems. No restrictions on the nature of the environment or on the strength of the coupling between system and environment need to be imposed. This free energy entering the Crooks theorem and the Jarzynski equality is closely related to the Hamiltonian of mean force that generalizes the classical statistical mechanical concept of the potential of mean force. DOI: 10.1103/PhysRevLett.102.210401 PACS numbers: 05.30.Àd, 05.70.Ln Since its formulation in 1997, the classical nonequilibrium work relation by Jarzynski [1] (now commonly referred to as the Jarzynski equality)has continued to raise questions and concerns on its range of validity and applicability. Here, w denotes the work performed on a system when some parameters of this system are changed according to a prescribed protocol. This work is given by the difference of the energies contained in the system at the end and at the beginning of the protocol. Initially, the system is supposed to be prepared in a thermal equilibrium state at the inverse temperature .The brackets hÁi denote a nonequilibrium average over many repetitions of this process, running under the same protocol. According to the Jarzynski equality, the average of the exponentiated negative work is independent of the details of the protocol and solely determined by the thermal equilibrium free energy difference ÁF between the initial equilibrium state and a hypothetical equilibrium state at the initial temperature and those parameter values that are reached at the end of the protocol. In the mentioned Letter [1], the validity of this equality was demonstrated within a classical statistical approach for isolated systems which initially are in the required equilibrium state at inverse temperature and also for classical systems that stay in weak contact with a thermal bath during the protocol. Considerable effort has been devoted to the development of the quantum version of Eq. (1) where p t f ;t 0 ðwÞ denotes the probability density function (PDF) of work performed by the parameter changes according to a protocol running between the initial time t 0 and final time t f . The PDF of work for the reversed protocol is denoted by p t 0 ;t f ðwÞ. All these attempts refer to quantum isolated or weakly coupled systems with Hamiltonian or Markovian dynamics, respectively [3][4][5][6][7][8][9]. The proof of the validity of Eqs. (1) and (2) in the quantum case with weak coupling, allowing for an otherwise general non-Markovian dynamics of the open quantum dynamics and arbitrary force protocols, was provided only recently in Ref.[10]. The applicability of Eqs. (1) and (2) to the case of weak coupling is consistent with the construction of quantum and classical statistical mechanics wh...

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Finite quantum dissipation: the challenge of obtaining specific heat

Cited by 131 publications

References 17 publications

Dissipative quantum systems and the heat capacity

Dissipative quantum systems and the heat capacity

Statistical description of small quantum systems beyond the weak-coupling limit

Fluctuations in open systems

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