Geometry and material effects in Casimir physics - Scattering theory

TL;DR

This paper presents a versatile scattering theory approach for calculating Casimir forces in complex geometries, materials, and media, enabling detailed analysis of stability and control of these quantum forces.

Contribution

It introduces a comprehensive scattering-based method that handles arbitrary shapes, media, and temperatures, advancing the precision and applicability of Casimir force calculations.

Findings

The method can analyze forces for any object configuration.

Electrodynamic Casimir forces cannot stabilize objects if all permittivities are higher or lower than the medium.

The approach combines statistical physics and scattering theory for diverse phenomena.

Abstract

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, to nonzero temperatures, and to spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. This approach, which combines methods of statistical physics and scattering theory, is well suited to analyze many diverse phenomena. We illustrate its power and versatility by a number of examples, which show how the interplay of geometry and material properties helps to understand and control Casimir forces. We also examine whether electrodynamic Casimir forces can lead to stable levitation. Neglecting permeabilities, we prove that any equilibrium position of objects subject to such forces is unstable if the permittivities of all objects are higher or lower than that of the enveloping medium; the former being the generic case for ordinary materials in vacuum.