Specific heat anomalies of small quantum systems subjected to finite baths

Hasegawa, Hideo

doi:10.1063/1.3669485

Cited by 24 publications

(37 citation statements)

References 26 publications

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“…There are several formulations and statements of the third law. We approach it from the behavior of the heat capacity near absolute zero, which aids us to resolve some puzzles raised in the literature such as the claimed negative specific heat near absolute zero even in well behaved systems [34], and address some concerns expressed by Hanggi, Ingold, Talkner, Weiss, et al [17,18,[35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law

Hsiang¹,

Chou²,

Subaşı³

et al. 2018

Phys. Rev. E

110

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In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of N strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are conceptually and factually unrelated issues. Entropy and entanglement will be the main theme of our second paper on this subject matter.

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Section: Introductionmentioning

confidence: 99%

Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law

Hsiang¹,

Chou²,

Subaşı³

et al. 2018

Phys. Rev. E

110

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“…More recently, studies have focused attention on baths endowed with finite resources, such as a finite number of harmonic oscillators distributed in a finite bandwidth, i.e. allowing for a non-zero infrared cut-off and a finite ultraviolet cut-off [5][6][7][8][9][10]. In particular, the dynamics of a target harmonic oscillator interacting via a linear and translationally invariant term with a bath, composed of a finite number of harmonic oscillators whose frequencies are all in a limited range, was studied in detail.…”

Section: Introductionmentioning

confidence: 99%

Effective microscopic models for sympathetic cooling of atomic gases

Onofrio

Sundaram

2015

Phys. Rev. A

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Thermalization of a system in the presence of a heat bath has been the subject of many theoretical investigations especially in the framework of solid-state physics. In this setting, the presence of a large bandwidth for the frequency distribution of the harmonic oscillators schematizing the heat bath is crucial, as emphasized in the Caldeira-Leggett model. By contrast, ultracold gases in atomic traps oscillate at well-defined frequencies and therefore seem to lie outside the Caldeira-Leggett paradigm. We introduce interaction Hamiltonians which allow us to adapt the model to an atomic physics framework. The intrinsic nonlinearity of these models differentiates them from the original Caldeira-Leggett model and calls for a nontrivial stability analysis to determine effective ranges for the model parameters. These models allow for molecular dynamics simulations of mixtures of ultracold gases, which is of current relevance for optimizing sympathetic cooling in degenerate Bose-Fermi mixtures.Comment: 14 pages, 7 figure

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“…However, if the system only interacts with a small heat bath with finite degrees of freedom, the system-bath interaction cannot be ignored. The properties of such finite system recently intrigue a lot of attentions from the aspects of both experiments [1,2] and theories [3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Noncanonical statistics of a finite quantum system with non-negligible system-bath coupling

Liu

et al. 2014

Phys. Rev. E

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The canonical statistics describes the statistical properties of an open system by assuming its coupling with the heat bath infinitesimal in comparison with the total energy in thermodynamic limit. In this paper, we generally derive a non-canonical distribution for the open system with a finite coupling to the heat bath, which deforms the energy shell to effectively modify the conventional canonical way. The obtained non-canonical distribution reflects the back action of system on the bath, and thus depicts the statistical correlations through energy fluctuations.

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Specific heat anomalies of small quantum systems subjected to finite baths

Cited by 24 publications

References 26 publications

Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law

Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law

Effective microscopic models for sympathetic cooling of atomic gases

Noncanonical statistics of a finite quantum system with non-negligible system-bath coupling

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