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TMF, 2018, Volume 195, Number 3, Pages 391–421 (Mi tmf9407)  

This article is cited in 1 scientific paper (total in 1 paper)

Vacuum and thermal energies for two oscillators interacting through a field

M. Bordag

Institute of Theoretical Physics, Leipzig University, Leipzig, Germany

Abstract: We consider a simple $(1+1)$-dimensional model for the Casimir–Polder interaction consisting of two oscillators coupled to a scalar field. We include dissipation in a first-principles approach by allowing the oscillators to interact with heat baths. For this system, we derive an expression for the free energy in terms of real frequencies. From this representation, we derive the Matsubara representation for the case with dissipation. We consider the case of vanishing intrinsic frequencies of the oscillators and show that the contribution from the zeroth Matsubara frequency is modified in this case and no problem with the laws of thermodynamics appears.

Keywords: Casimir–Polder force, temperature, dissipation, heat bath.

DOI: https://doi.org/10.4213/tmf9407

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English version:
Theoretical and Mathematical Physics, 2018, 195:3, 834–860

Bibliographic databases:

Document Type: Article
PACS: 05.40.-a
Received: 31.05.2017
Revised: 16.07.2017

Citation: M. Bordag, “Vacuum and thermal energies for two oscillators interacting through a field”, TMF, 195:3 (2018), 391–421; Theoret. and Math. Phys., 195:3 (2018), 834–860

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  • https://doi.org/10.4213/tmf9407
  • http://mi.mathnet.ru/eng/tmf/v195/i3/p391

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bordag M., Klimchitskaya G.L., Mostepanenko V.M., “Nonperturbative Theory of Atom-Surface Interaction: Corrections At Short Separations”, J. Phys.-Condes. Matter, 30:5 (2018), 055003  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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