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

Claudio Bórquez, Byron Droguett

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 $ζ$--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.

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 --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.
Paper Structure (5 sections, 41 equations, 4 figures)

This paper contains 5 sections, 41 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Rough membrane in Hořava-Lifshitz theory
  3. Casimir effect: $\zeta$--function regularization
  4. Casimir effect at finite temperature
  5. Conclusions

Figures (4)

  • Figure 1: Casimir force density versus separation distance $a$. The solid curves represent the case without roughness ($h=0$) and the dashed curves represent the case with roughness ($h\neq 0$), both for different values of the anisotropic scaling factor $z=1,3,5$.
  • Figure : (a)
  • Figure : (a)
  • Figure : (b)