Casimir Force for Absorbing Media in an Open Quantum System Framework: Scalar Model

TL;DR

This paper models the Casimir force between dissipative, finite-width mirrors at finite temperature within an open quantum system framework, revealing both vacuum and thermal noise contributions in a simplified 1+1D setting.

Contribution

It introduces a novel approach to compute the Casimir force for absorbing media using open quantum system theory, including dissipation and thermal effects.

Findings

The Casimir force has vacuum and Langevin noise contributions.

Both contributions are necessary to recover the Lifshitz formula in 1+1D.

The spectral density of the environment relates to mirror properties.

Abstract

In this article we compute the Casimir force between two finite-width mirrors at finite temperature, working in a simplified model in 1+1 dimensions. The mirrors, considered as dissipative media, are modeled by a continuous set of harmonic oscillators which in turn are coupled to an external environment at thermal equilibrium. The calculation of the Casimir force is performed in the framework of the theory of quantum open systems. It is shown that the Casimir interaction has two different contributions: the usual radiation pressure from vacuum, which is obtained for ideal mirrors without dissipation or losses, and a Langevin force associated with the noise induced by the interaction between dielectric atoms in the slabs and the thermal bath. Both contributions to the Casimir force are needed in order to reproduce the analogous of Lifshitz formula in 1+1 dimensions. We also discuss the relation between the electromagnetic properties of the mirrors and the spectral density of the environment