Vacuum energy for generalised Dirac combs at $T=0$

Abstract

The quantum vacuum energy for a hybrid comb of Dirac $\delta$-${\delta }^{\prime }$ potentials is computed using the energy of the single $\delta$-${\delta }^{\prime }$ potential over the real line that makes up the comb. The zeta function of a comb periodic potential is the continuous sum of zeta functions over the dual primitive cell of Bloch quasi-momenta. The result obtained for the quantum vacuum energy is non-perturbative in the sense that the energy function is not analytical for small couplings

13 pages, 3 figures. Bibliography and Acknowledgements minor corrections have been included. Some changes have been included in the first four sections

References in corpus (2)

• Casimir Effect and Global Theory of Boundary Conditions
• $\delta -{\delta }^{\prime }$ generalized Robin boundary conditions and quantum vacuum fluctuations

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