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The Casimir effect as a sum-over-modes in dissipative systems

The aim of this paper is to show that within the open-system framework the sum-over-modes approach á la Casimir leads to the Lifshitz formula for the Casimir free energy. A general result applicable to arbitrary geometries is obtained through the use of Ford, Lewis, & O'Connell's remarkable formula. Additionally, we address the possibility for obtaining the Casimir energy as a sum over complex "modes". We show in this case that the standard sum-over-modes formula must be suitably generalized to avert unphysical complex energies. Finally, we apply our results to several standard examples.

preprint2012arXivOpen access
Francesco IntravaiaRyan Behunin
quant-ph
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Open access2 authors1 topic
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Francesco IntravaiaRyan Behunin

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