Casimir Effect of rough plates under a magnetic field in Ho\v{r}ava-Lifshitz theory

TL;DR

This paper studies the Casimir effect between rough plates in Hořava-Lifshitz theory, analyzing how magnetic fields and surface roughness influence quantum fluctuations using perturbation and zeta-function regularization.

Contribution

It introduces a novel approach to incorporate surface roughness as a potential in the Casimir effect within Hořava-Lifshitz theory, considering magnetic fields and anisotropic scaling.

Findings

Derived the spectrum of quantum fluctuations with roughness and magnetic field effects.

Applied perturbation theory and zeta-function regularization to obtain results.

Illustrated the method with plates under periodic boundary conditions.

Abstract

We investigate the Casimir effect for parallel plates within the framework of Ho\v{r}ava-Lifshitz theory in $3+1$ dimensions, considering the effects of roughness, anisotropic scaling factor, and an uniform constant magnetic field. Quantum fluctuations are induced by an anisotropic charged-scalar quantum field subject to Dirichlet boundary conditions. To incorporate surface roughness, we apply a coordinate transformation to flatten the plates, treating the remaining roughness terms as potential. The spectrum is derived using perturbation theory and regularized with the $\zeta$-function method. As an illustrative example, we consider plates with periodic boundary conditions.