# Geometry and material effects in Casimir physics – Scattering theory

### Sahand Jamal Rahi ^{1, 2}, Thorsten Emig ^{3}, Robert L. Jaffe ^{1}

#### Casimir Physics (2011) vol. 834, 129-174

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.

- 1. Department of Physics,

Massachusetts Institute of Technology - 2. Center for Studies in Physics and Biology,

The Rockefeller University - 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),

CNRS : UMR8626 – Université Paris XI - Paris Sud