Vacuum fluctuations in the presence of nonlinear boundary conditions

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.

16 pages, 1 figure, LaTeX

References in corpus (6)

• Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit
• A new renormalization approach to the Dirichlet Casimir effect for ϕ^4 theory in (1+1) dimensions
• Boundary one-point function, Casimir energy and boundary state formalism in D+1 dimensional QFT
• Casimir effect with dynamical matter on thin mirrors
• Derivative expansion for the boundary interaction terms in the Casimir effect: generalized $\delta$-potentials
• Weak Coupling Casimir Energies for Finite Plate Configurations

Cited by in corpus (1)

• Fluctuational electrodynamics for nonlinear media