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arXiv · 1110.0421

Weyl problem and Casimir effects in spherical shell geometry

Eugene B. Kolomeisky·Hussain Zaidi·Luke Langsjoen·Joseph P. Straley
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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.

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Eugene B. Kolomeisky, Hussain Zaidi, Luke Langsjoen, Joseph P. Straley. 2013-04-16. Weyl problem and Casimir effects in spherical shell geometry. https://doi.org/10.1103/physreva.87.042519

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