Vacuum fluctuations in the presence of nonlinear boundary conditions

TL;DR

This paper investigates how nonlinear boundary conditions on mirrors affect vacuum fluctuations and Casimir energy for a massless scalar field, using perturbative methods for weak interactions.

Contribution

It introduces a perturbative approach to analyze Casimir energy with nonlinear boundary conditions, extending traditional linear models.

Findings

Derived approximate Casimir energy expressions for weak nonlinear interactions.

Discussed alternative expansion schemes for strong coupling regimes.

Provided insights into the impact of nonlinear boundary conditions on vacuum fluctuations.

Abstract

We consider a system consisting of a quantum, massless, real scalar field, in the presence of nonlinear mirrors: infinite parallel planes, upon which the field satisfies nonlinear boundary conditions. The latter are implemented by non-quadratic interaction vertices, strictly localized on the mirrors. By using the appropriate perturbative expansions, we obtain approximate expressions for the Casimir energy corresponding to weak coupling, regarding the strength of the interaction terms. We also comment on an alternative expansion scheme that may be useful when the weak coupling expansion is not justified.