The Casimir force at high temperatureP. R. Buenzli and Ph. A. Martin
Institute of Theoretical Physics, Swiss Federal Institute of Technology, EPFL CH-1015 Lausanne, Switzerland
received 20 June 2005; accepted 26 July 2005
published online 31 August 2005
The standard expression of the high-temperature Casimir force between perfect conductors is obtained by imposing macroscopic boundary conditions on the electromagnetic field at metallic interfaces. This force is twice larger than that computed in microscopic classical models allowing for charge fluctuations inside the conductors. We present a direct computation of the force between two quantum plasma slabs in the framework of non-relativistic quantum electrodynamics including quantum and thermal fluctuations of both matter and field. In the semi-classical regime, the asymptotic force at large slab separation is identical to that found in the above purely classical models, which is therefore the right result. We conclude that when calculating the Casimir force at non-zero temperature, fluctuations inside the conductors cannot be ignored. Aspects of this subject are treated in a companion letter by JANCOVICI B. and SAMAJ L., Casimir force between two ideal-conductor walls revisited (Europhys. Lett., 72 (2005) 35).
05.30.-d - Quantum statistical mechanics.
12.20.-m - Quantum electrodynamics.
11.10.Wx - Finite-temperature field theory.
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