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Cited by 87Advanced Thermodynamics and Statistical MechanicsQuantum Mechanics and ApplicationsQuantum optics and atomic interactions

Master equation for strongly interacting systems

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Carmichael, H J, Walls, D F·1973·Journal of Physics A: Mathematical, Nuclear and General
DOI 10.1088/0305-4470/6/10/014
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Abstract

A dissipating system consisting of two strongly interacting subsystems, each coupled to its respective thermal reservoir is considered. The usual method for obtaining a master equation for the reduced density operator of such a system is to assume the factorization of this density operator in the derivation of the irreversible term, retaining the coupling in the reversible term alone. This approach has the serious limitation that it fails to preserve detailed balance in general and yields an incorrect canonical form for the stationary solution of the density operator. A general approach, based on the introduction of a new interaction picture, is presented. This method is illustrated by applying it to a coupled boson system and to a two-level atom interacting with a single mode of the electromagnetic field.

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Crossref · 10.1088/0305-4470/6/10/014

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  • In an equilibrium situation, the global master equation results in a Gibbs state with respect to the system Hamiltonian.

    “In an equilibrium situation (i.e.baths at equal temperatures and time-independent Hamiltonian) the global master equation results in the desired steady state which is given by a Gibbs state with respect to the system Hamiltonian [1,60]”

    From Markovian master equations for quantum thermal machines: Local versus global approach (2017) · cites this paper as [60]

  • In an equilibrium situation, the local master equation results in a product of Gibbs states with respect to the sub-system Hamiltonians.

    “The local approach on the other hand results in a product of Gibbs states with respect to the sub-system Hamiltonians [60].”

    From Markovian master equations for quantum thermal machines: Local versus global approach (2017) · cites this paper as [60]

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Cites

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Research works printed but not linked: 5

  1. Haken H 1969 Handb. Phys. 25/2c 1-320 (Berlin: Springer-Verlag)
  2. Jaynes E T and Cummings F W 1963 Proc. IRE 51 89-109
  3. Loudon R 1969 Quantum Optics (Proc. Int. School of Physics 'Enrico Fermi') vol 42, ed R J Glauber (New Louisell W H 1964 Radiation and Noise in Quantum Electronics (New York: McGraw-Hill) -1969 Quantum Optics (Proc. Int. School of Physis 'Enrico Fermi') vol42, ed R J Glauber (New York: Louisell W H, Yariv A and Siegman A E 1961 Phys. Rev. 124 1646-54
  4. Pike E R 1970 Quantum Optics (Proc. Scottish Universities Summer School in Physics, 1969) ed
  5. Weidlich W and Haake F 1965a Z. Phys. 185 30-47 York: Academic Press) pp 297-320 Academic Press) pp 68LL742 A Maitland (New York: Academic Press) pp 127-76

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Related

Authors
Carmichael, H. J., & Walls, D. F.
Affiliations
University of Waikato (NZ)
ORCID
Carmichael, H J
Venue
Journal of Physics A: Mathematical, Nuclear and General
Publisher
IOP Publishing
Published
1973-10-01
Volume
6
Issue
10
Pages
1552-1564
ISSN
0301-0015 (ISSN-L)
DOI
10.1088/0305-4470/6/10/014
OpenAlex
W1965470034
Cited by
87
References
15
Citations by year
2025: 4 · 2024: 5 · 2023: 2 · 2022: 12 · 2021: 6 · 2020: 3 · 2019: 2 · 2018: 2 · 2017: 2 · 2016: 2 · 2015: 5 · 2014: 2 · 2013: 5 · 2012: 4
FWCI
2.64
Type
journal article
Language
en
Open access
Locations
Journal of Physics A Mathematical Nuclear and General (publishedVersion)
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 Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
Keywords
master equation, dissipative systems, reduced density operator, detailed balance, interaction picture, two-level atom, atom-field interaction

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