Thermal Casimir effect in $\kappa$-Minkowski space-time

TL;DR

This paper investigates how non-commutative $ppa$-Minkowski space-time modifies the thermal Casimir effect, revealing enhanced attractive forces and establishing bounds on the deformation parameter with potential experimental implications.

Contribution

It provides the first detailed calculation of thermal Casimir effects in $ppa$-deformed space-time, including thermodynamic consistency and bounds on the deformation parameter.

Findings

Space-time non-commutativity increases Casimir attraction.

Thermodynamic laws are preserved in $ppa$-deformed space.

Upper bound on deformation parameter is $a \u2264 10^{-18}m$.

Abstract

We study the finite temperature Casimir effect for parallel plates in the $\kappa$-Minkowski space-time. Using the Matsubara formalism and imposing the Dirichlet boundary conditions on a massless $\kappa$-scalar field, we compute the $\kappa$-deformed corrections to thermal Casimir free energy, pressure, entropy, and internal energy. Our results demonstrate that space-time non-commutativity enhances the attractive nature of the thermal Casimir force while preserving thermodynamic consistency; the system satisfies the Nernst theorem and laws of thermodynamics remain intact in $\kappa$-deformed space-time. Our analysis yields an upper bound on the deformation parameter as $a\leq10^{-18}m$. Furthermore, our results indicate that non-commutative effects become experimentally observable in Casimir effect studies when the ratio of the non-commutative scale to plate separation satisfies $a/L\leq 10^{-12}$. We also obtain the expression for Stefan-Boltzmann's law in $\kappa$-Minkowski space-time.