Vacuum and thermal energies for two oscillators interacting through a~field
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 391-421
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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.
@article{TMF_2018_195_3_a3,
author = {M. Bordag},
title = {Vacuum and thermal energies for two oscillators interacting through a~field},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {391--421},
publisher = {mathdoc},
volume = {195},
number = {3},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a3/}
}
M. Bordag. Vacuum and thermal energies for two oscillators interacting through a~field. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 391-421. http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a3/