Casimir effect of a rough membrane in 2+1 Horava-Lifshitz theory

Abstract

We investigate the Casimir effect of a rough membrane within the framework of the Horava-Lifshitz theory in 2+1 dimensions. Quantum fluctuations are induced by an anisotropic scalar field subject to Dirichlet boundary conditions. We implement a coordinate transformation to render the membrane completely flat, treating the remaining terms associated with roughness as a potential. The spectrum is obtained through perturbation theory and regularized using the $\zeta$--function method. We present an explicit example of a membrane with periodic border. Additionally, we consider the effect of temperature. Our findings reveal that the Casimir energy and force depend on roughness, the anisotropic scaling factor and temperature.

Minor correction in introduction

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Cited by in corpus (4)

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• One-Loop Correction to the Casimir Energy in Lorentz-Violating ${\varphi }^4$ Theory with Rough Membrane Boundaries
• One-Loop Quantum Corrections to the Casimir Effect for Smoothly Rough Plates in the Low-Temperature Regime