Finite Temperature Casimir Effect for a Massless Fractional Klein-Gordon field with Fractional Neumann Conditions

TL;DR

This paper investigates the finite temperature Casimir effect for a fractional Klein-Gordon field with novel fractional Neumann boundary conditions, revealing a transition from attractive to repulsive forces and analyzing temperature effects.

Contribution

It introduces fractional Neumann boundary conditions for the Klein-Gordon field, enabling interpolation between Dirichlet and Neumann conditions and analyzing their impact on the Casimir effect.

Findings

Casimir force can switch from attractive to repulsive depending on fractional boundary parameters.

High temperature Casimir energy becomes boundary-condition independent.

Temperature inversion symmetry holds under various fractional boundary conditions.

Abstract

This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed.