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Cited by 38Advanced Thermodynamics and Statistical MechanicsQuantum and electron transport phenomenaQuantum many-body systems

Microscopic theory of a nonequilibrium open bosonic chain

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Santos, Jader P., Landi, Gabriel T.·2016·Physical Review E
DOI 10.1103/physreve.94.062143
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Abstract

Quantum master equations form an important tool in the description of transport problems in open quantum systems. However, they suffer from the difficulty that the shape of the Lindblad dissipator depends sensibly on the system Hamiltonian. Consequently, most of the work done in this field has focused on phenomenological dissipators which act locally on different parts of the system. In this paper we show how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials. We show that even though the bath coupling is local, the effective Lindblad dissipator stemming from this interaction is inherently nonlocal, affecting all normal modes of the system. We then use this formalism to study the current of particles and energy through the system and find that they have the structure of Landauer's formula, with the bath spectral density playing the role of the transfer integral. Finally, we consider infinitesimal temperature and chemical potential gradients and show that the currents satisfy Onsager's reciprocal relations, which is a consequence of the fact that the microscopic quantum dynamics obeys detailed balance.

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Crossref · 10.1103/physreve.94.062143

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  • For fermionic baths, the analogous local-validity inequalities are usually not fulfilled at low temperatures due to the step-like behavior of the Fermi-Dirac distribution.

    “For fermionic baths, equations analogous to equations (17) can be derived.These are usually not fulfilled at low temperatures due to the step-like behavior of the Fermi-Dirac distribution [23,66].”

    From Markovian master equations for quantum thermal machines: Local versus global approach (2017) · cites this paper as [66]

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Research works printed but not linked: 2

  1. [29]L. Onsager, Physical Review 38 , 2265 (1931). http://prola.aps.org/abstract/PR/v38/i12/p2265%7B_%7D1
  2. [30]L. Onsager, Physical Review 37 , 405 (1931). http://prola.aps.org/abstract/PR/v37/i4/p405%7B_%7D1

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Authors
Santos, J. P., & Landi, G. T.
Affiliations
  • Universidade Federal do ABC (BR)
  • Universidade de São Paulo (BR)
ORCID
Venue
Physical Review E
Publisher
American Physical Society (APS)
Published
2016-12-28
Volume
94
Issue
6
Pages
062143-062143
ISSN
  • 2470-0045 (ISSN-L)
  • 2470-0053
DOI
10.1103/physreve.94.062143
OpenAlex
W2537697587
Cited by
38
References
51
Citations by year
2026: 2 · 2025: 4 · 2024: 2 · 2023: 1 · 2022: 2 · 2021: 6 · 2020: 5 · 2019: 6 · 2018: 4 · 2017: 6
FWCI
3.02
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. E (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Fundação de Amparo à Pesquisa do Estado de São Paulo (2016/08721-7)
  • Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
open quantum systems, tight-binding chain, Landauer formula, particle current, energy current, Onsager reciprocal relations, detailed balance, bath spectral density, quantum transport

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