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arXiv · 2312.01997

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

Claudio Bórquez·Byron Droguett
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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.

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Claudio Bórquez, Byron Droguett. 2023-12-04. Casimir effect of a rough membrane in 2+1 Horava-Lifshitz theory. https://doi.org/10.1140/epjc%2Fs10052-024-12420-6

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