Weyl problem and Casimir effects in spherical shell geometry
Abstract
We compute the generic mode sum that quantifies the effect on the spectrum of a harmonic field when a spherical shell is inserted into vacuum. This encompasses a variety of problems including the Weyl spectral problem and the Casimir effect of quantum electrodynamics. This allows us to resolve several long-standing controversies regarding the question of universality of the Casimir self-energy; the resolution comes naturally through the connection to the Weyl problem. Specifically we demonstrate that in the case of a scalar field obeying Dirichlet or Neumann boundary conditions on the shell surface the Casimir self-energy is cutoff-dependent while in the case of the electromagnetic field perturbed by a conductive shell the Casimir self-energy is universal. We additionally show that an analog non-relativistic Casimir effect due to zero-point magnons takes place when a non-magnetic spherical shell is inserted inside a bulk ferromagnet.
Keywords
Cite
@article{arxiv.1110.0421,
title = {Weyl problem and Casimir effects in spherical shell geometry},
author = {Eugene B. Kolomeisky and Hussain Zaidi and Luke Langsjoen and Joseph P. Straley},
journal= {arXiv preprint arXiv:1110.0421},
year = {2013}
}
Comments
9 pages, minor changes, additional references added, version to be published in Phys. Rev. A