Using boundary methods to compute the Casimir energy

Details Using boundary methods to compute the Casimir energy Using boundary methods to compute the Casimir energy

2010-03-10

arxiv.org/abs/1003.2011v1

Physics

Quantum Physics

To be published in the Proceedings of QFEXT09, Norman, OK.

Scientific paper

We discuss new approaches to compute numerically the Casimir interaction energy for waveguides of arbitrary section, based on the boundary methods traditionally used to compute eigenvalues of the 2D Helmholtz equation. These methods are combined with the Cauchy's theorem in order to perform the sum over modes. As an illustration, we describe a point-matching technique to compute the vacuum energy for waveguides containing media with different permittivities. We present explicit numerical evaluations for perfect conducting surfaces in the case of concentric corrugated cylinders and a circular cylinder inside an elliptic one.

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