The Casimir effect as a sum-over-modes in dissipative systems
arXiv:1209.6072 · doi:10.1103/PhysRevA.86.062517
Abstract
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.
20 pages, 3 figures