https://doi.org/10.1140/epjc/s10052-024-12420-6
Regular Article - Theoretical Physics
Casimir effect of a rough membrane in 2 + 1 Hořava–Lifshitz theory
1
Department of Physics, Universidad de Antofagasta, 1240000, Antofagasta, Chile
2
Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad Santo Tomás, Sede Arica, Arica, Chile
Received:
7
December
2023
Accepted:
8
January
2024
Published online:
21
January
2024
We investigate the Casimir effect of a rough membrane within the framework of the Hořava–Lifshitz theory in 
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.
© The Author(s) 2024
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