Casimir effect of a rough membrane in an Aether-like Lorentz-violating scenario

TL;DR

This paper investigates how Lorentz-violating Aether vectors influence the Casimir effect of a rough membrane, revealing that Aether vectors significantly impact the main effect while roughness affects secondary terms, including finite-temperature considerations.

Contribution

It introduces a perturbative approach to analyze the Casimir effect of a rough membrane in Lorentz-violating theories with explicit Aether vectors, highlighting their dominant influence.

Findings

Aether vectors significantly alter the dominant Casimir term.

Roughness primarily affects secondary contributions.

Finite-temperature effects are also analyzed.

Abstract

We explore the Casimir effect of a rough membrane within the framework of theories that break Lorentz symmetry. We consider two constant Aether vectors: one timelike and other spacelike, simultaneously. We employ an appropriate change of coordinates such that the membrane assumes a completely flat border and the remaining terms associated with the roughness are considered as part of the potential. Quantum fluctuations are induced by a scalar quantum field subject to Dirichlet boundary conditions. The spectrum is obtained through perturbation theory and regularized using the $\zeta$--function method. We provide an explicit example of a membrane with periodic boundaries. The presence of Aether vectors has a significant impact on the dominant term of the Casimir effect, while roughness only affects the secondary terms. Additionally, we examine the finite-temperature case.