dorsal/arxiv
View SchemaSemiclassical Casimir Energies at Finite Temperature
| Authors | Martin Schaden, Larry Spruch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0012082 |
| URL | https://arxiv.org/abs/quant-ph/0012082 |
| DOI | 10.1103/PhysRevA.65.022108 |
Abstract
We study the dependence on the temperature T of Casimir effects for a range of systems, and in particular for a pair of ideal parallel conducting plates, separated by a vacuum. We study the Helmholtz free energy, combining Matsubara's formalism, in which the temperature appears as a periodic Euclidean fourth dimension of circumference 1/T, with the semiclassical periodic orbital approximation of Gutzwiller. By inspecting the known results for the Casimir energy at T=0 for a rectangular parallelepiped, one is led to guess at the expression for the free energy of two ideal parallel conductors without performing any calculation. The result is a new form for the free energy in terms of the lengths of periodic classical paths on a two-dimensional cylinder section. This expression for the free energy is equivalent to others that have been obtained in the literature. Slightly extending the domain of applicability of Gutzwiller's semiclassical periodic orbit approach, we evaluate the free energy at T>0 in terms of periodic classical paths in a four-dimensional cavity that is the tensor product of the original cavity and a circle. The validity of this approach is at present restricted to particular systems. We also discuss the origin of the classical form of the free energy at high temperatures.
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"abstract": "We study the dependence on the temperature T of Casimir effects for a range\nof systems, and in particular for a pair of ideal parallel conducting plates,\nseparated by a vacuum. We study the Helmholtz free energy, combining\nMatsubara\u0027s formalism, in which the temperature appears as a periodic Euclidean\nfourth dimension of circumference 1/T, with the semiclassical periodic orbital\napproximation of Gutzwiller. By inspecting the known results for the Casimir\nenergy at T=0 for a rectangular parallelepiped, one is led to guess at the\nexpression for the free energy of two ideal parallel conductors without\nperforming any calculation. The result is a new form for the free energy in\nterms of the lengths of periodic classical paths on a two-dimensional cylinder\nsection. This expression for the free energy is equivalent to others that have\nbeen obtained in the literature. Slightly extending the domain of applicability\nof Gutzwiller\u0027s semiclassical periodic orbit approach, we evaluate the free\nenergy at T\u003e0 in terms of periodic classical paths in a four-dimensional cavity\nthat is the tensor product of the original cavity and a circle. The validity of\nthis approach is at present restricted to particular systems. We also discuss\nthe origin of the classical form of the free energy at high temperatures.",
"arxiv_id": "quant-ph/0012082",
"authors": [
"Martin Schaden",
"Larry Spruch"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.022108",
"title": "Semiclassical Casimir Energies at Finite Temperature",
"url": "https://arxiv.org/abs/quant-ph/0012082"
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