Geometry and material effects in Casimir physics - Scattering theory

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.

44 pages, 11 figures, to appear in upcoming Lecture Notes in Physics volume in Casimir physics

References in corpus (22)

• Casimir forces between arbitrary compact objects
• The Casimir effect within scattering theory
• Measurement of the Casimir force between a gold sphere and silicon surface with nanoscale trench arrays
• Casimir-Lifshitz Theory and Metamaterials
• Control of the Casimir force by the modification of dielectric properties with light
• Casimir forces in a T operator approach
• Casimir repulsion between metallic objects in vacuum
• The Casimir force and the quantum theory of lossy optical cavities
• Casimir Forces between Compact Objects: I. The Scalar Case
• Anomalies in electrostatic calibrations for the measurement of the Casimir force in a sphere-plane geometry
• Demonstration of the difference Casimir force for samples with different charge carrier densities
• Casimir edge effects
• Exact Casimir interaction between eccentric cylinders
• Precision measurement of the Casimir-Lifshitz force in a fluid
• Comment on the sign of the Casimir force
• Casimir manipulations: The orientation dependence of fluctuation-induced forces
• Transition from Casimir to van der Waals force between macroscopic bodies
• Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit
• Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders
• The Casimir effect as scattering problem
• Interplay between geometry and temperature for inclined Casimir plates
• From multiple scattering to van der Waals interactions: exact results for eccentric cylinders

Cited by in corpus (5)

• Van der Waals torque and force between dielectrically anisotropic layered media
• Topologically protected Casimir effect for lattice fermions
• Thermal Issues in Casimir Forces Between Conductors and Semiconductors
• Casimir Forces via Worldline Numerics: Method Improvements and Potential Engineering Applications
• Exact Electromagnetic Casimir Energy of a Disk Opposite a Plane