Geodesic
Vacuum and thermal energies for two oscillators interacting through a field
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 391-421 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2018},
     volume = {195},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a3/}
}
TY  - JOUR
AU  - M. Bordag
TI  - Vacuum and thermal energies for two oscillators interacting through a field
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2018
SP  - 391
EP  - 421
VL  - 195
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a3/
LA  - ru
ID  - TMF_2018_195_3_a3
ER  - 
%0 Journal Article
%A M. Bordag
%T Vacuum and thermal energies for two oscillators interacting through a field
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2018
%P 391-421
%V 195
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a3/
%G ru
%F 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/

[1] V. B. Bezerra, G. L. Klimchitskaya, V. M. Mostepanenko, “Thermodynamical aspects of the Casimir force between real metals at nonzero temperature”, Phys. Rev. A, 65:5 (2002), 052113, 7 pp. | DOI

[2] G. L. Klimchitskaya, V. M. Mostepanenko, “Conductivity of dielectric and thermal atom-wall interaction”, J. Phys. A: Math. Theor., 41:31 (2008), 312002, 9 pp. | DOI

[3] G. L. Klimchitskaya, V. M. Mostepanenko, “Casimir free energy and pressure for magnetic metal films”, Phys. Rev. B, 94:4 (2016), 045404, 13 pp. | DOI

[4] J. Schwinger, L. L. DeRaad, Jr., K. A. Milton, “Casimir effect in dielectrics”, Ann. Phys., 115:1 (1978), 1–23 | DOI | MR

[5] D. Kupiszewska, “Casimir effect in absorbing media”, Phys. Rev. A, 46:5 (1992), 2286–2294 | DOI

[6] F. S. S. Rosa, D. A. R. Dalvit, P. W. Milonni, “Electromagnetic energy, absorption, and Casimir forces: uniform dielectric media in thermal equilibrium”, Phys. Rev. A, 81:3 (2010), 033812, 12 pp. | DOI

[7] F. S. S. Rosa, D. A. R. Dalvit, P. W. Milonni, “Electromagnetic energy, absorption, and Casimir forces. II. Inhomogeneous dielectric media”, Phys. Rev. A, 84:5 (2011), 053813, 13 pp. | DOI

[8] F. C. Lombardo, F. D. Mazzitelli, A. E. Rubio López, “Casimir force for absorbing media in an open quantum system framework: scalar model”, Phys. Rev. A, 84:5 (2011), 052517, 12 pp. | DOI

[9] P. R. Berman, G. W. Ford, P. W. Milonni, “Nonperturbative calculation of the London–van der Waals interaction potential”, Phys. Rev. A, 89:2 (2014), 022127, 4 pp. | DOI

[10] M. A. Braun, “Ob energii Kazimira v srede s dispersiei i pogloscheniem v ramkakh podkhoda diagonalizatsii Fano”, TMF, 190:2 (2017), 277–292 | DOI | DOI | MR

[11] H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems, Oxford Univ. Press, New York, 2002 | MR

[12] M. Bordag, “Drude model and Lifshitz formula”, Eur. Phys. J. C, 71 (2011), 1788, 12 pp. | DOI

[13] F. Intravaia, R. Behunin, “Casimir effect as a sum over modes in dissipative systems”, Phys. Rev. A, 86:6 (2012), 062517 pp. | DOI

[14] U. Fano, “Effects of configuration interaction on intensities and phase shifts”, Phys. Rev., 124:6 (1961), 1866–1878 | DOI

[15] B. Huttner, S. M. Barnett, “Quantization of the electromagnetic field in dielectrics”, Phys. Rev. A, 46:7 (1992), 4306–4322 | DOI

[16] H. B. Callen, T. A. Welton, “Irreversibility and generalized noise”, Phys. Rev., 83:1 (1951), 34–40 | DOI | MR

[17] G. W. Ford, J. T. Lewis, R. F. O'Connell, “Quantum Langevin equation”, Phys. Rev. A, 37:11 (1988), 4419–4428 | DOI | MR

[18] G. W. Ford, J. T. Lewis, R. F. O'Connell, “Quantum oscillator in a blackbody radiation field”, Phys. Rev. Lett., 55:21 (1985), 2273–2276 | DOI | MR

[19] M. Bordag, “Vacuum energy in smooth background fields”, J. Phys. A: Math. Gen., 28:3 (1995), 755–765 | DOI | MR

[20] M. J. Renne, “Retarded Van der Waals interaction in a system of harmonic oscillators”, Physica, 53:2 (1971), 193–209 | DOI

[21] M. J. Renne, B. R. A. Nijboer, “Microscopic derivation of macroscopic Van der Waals forces”, Chem. Phys. Lett., 1:8 (1967), 317–320 | DOI

[22] M. Bordag, J. M. Muñoz-Castañeda, “Dirac lattices, zero-range potentials and self-adjoint extension”, Phys. Rev. D, 91:6 (2015), 065027, 19 pp. | MR