Casimir piston of real materials and its application to multilayer models

Abstract

In this article, we derive the formula for the Casimir force acting on a piston made of real material moving inside a perfectly conducting rectangular box. It is shown that by taking suitable limits, one recovers the formula for the Casimir force acting on a perfectly conducting piston or an infinitely permeable piston. The Lifshitz formula for finite temperature Casimir force acting on parallel plates made of real materials is re-derived by considering the five-layer model in the context of the piston approach. It is observed that the divergences of the Casimir force will only cancel under certain conditions, for example, when the regions separated by the plates are filled with media of the same refractive index.

Casimir Effect Across a Layered Medium

“…This result then coincides with the corresponding result derived in Ref. 1 whereas the results obtained in Refs. 2 and 3 correspond to plates with R q L(R) = −1 and R q L(R) = 1, respectively.…”

Casimir forces in multilayer magnetodielectrics with both gain and loss

“…One can check that in the absence of amplification, our expression (30) tends to a known result for lossy media [2,64]. In the limit where the two perfect conductors are brought to infinity (i.e., d 1 , d 3 → ∞), Eq.…”

Casimir Effect Associated with Fractional Klein–Gordon Field

“…He demonstrated that in the case of a massless scalar field with Dirichlet boundary conditions, a finite attractive Casimir force without the surface divergence is obtained due to the cancelation of the divergent part of the Casimir force acting in the two regions separated by the piston. This result leads to a surge in the studying of the Casimir force on pistons with various geometric configurations and boundary conditions [71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87] . Casimir force on a rectangular piston in the spacetime with extra compactified dimensions has also been studied [88][89][90][91][92][93] .…”

“…For Casimir effect on an n-dimensional (n = 1, 2 or 3) rectangular piston with mixed boundary conditions, namely with one surface having Dirichlet condition, and the other with Neumann condition, the resulting force is repulsive. 78 Other possible ways of obtaining a repulsive Casimir force have also been discussed 79,83,85,86,92,96 . In particular, the Casimir force of fractional Klein-Gordon field acting on a piston with fractional boundary conditions can be repulsive 85,96 .…”