Accounting for dissipation in the scattering approach to the Casimir energy

TL;DR

This paper extends the scattering approach to Casimir energy calculations by explicitly incorporating dissipation, ensuring the formula remains valid even in dissipative media, and leverages unitarity of scattering processes.

Contribution

It introduces a scattering formula for Casimir energy that explicitly accounts for dissipation channels, broadening the applicability to dissipative environments.

Findings

The derived formula remains valid with dissipative media.

Dissipation channels are explicitly included in the scattering approach.

The approach leverages unitarity to handle dissipation effects.

Abstract

We take dissipation into account in the derivation of the Casimir energy formula between two objects placed in a surrounding medium. The dissipation channels are considered explicitly in order to take advantage of the unitarity of the full scattering processes. We demonstrate that the Casimir energy is given by a scattering formula expressed in terms of the scattering amplitudes coupling internal channels and taking dissipation into account in an implicit way. We prove that this formula is also valid when the surrounding medium is dissipative.