Casimir energy and entropy between dissipative mirrors

TL;DR

This paper investigates how dissipation and temperature influence the Casimir effect between parallel slabs, analyzing entropy behavior at low temperatures and deriving a mode sum formula for dissipative materials.

Contribution

It provides a detailed analysis of the Casimir entropy at low temperatures considering dissipation, and introduces a mode sum formula for dissipative slabs interpreted as damped oscillators.

Findings

Casimir entropy approaches zero as temperature approaches zero.

Reflection coefficients at low frequencies determine entropy behavior.

A mode sum formula for dissipative slabs is derived.

Abstract

We discuss the Casimir effect between two identical, parallel slabs, emphasizing the role of dissipation and temperature. Starting from quite general assumptions, we analyze the behavior of the Casimir entropy in the limit T->0 and link it to the behavior of the slab's reflection coefficients at low frequencies. We also derive a formula in terms of a sum over modes, valid for dissipative slabs that can be interpreted in terms of a damped quantum oscillator.