The `Friction' of Vacuum, and other Fluctuation-Induced Forces

TL;DR

This paper explores the fluctuation-induced forces such as the Casimir effect and van der Waals interactions, analyzing how boundaries and shape influence these phenomena and their dynamic aspects using a path integral approach.

Contribution

It introduces a path integral formalism to study fluctuation-induced forces for arbitrary boundary shapes, revealing shape-dependent effects on effective mass, dissipation, and resonance modes.

Findings

Effective mass depends on shape and becomes anisotropic.

Motion induces dissipation and damping via photon emission.

Resonant cavity modes can be excited by boundary motion.

Abstract

The static Casimir effect describes an attractive force between two conducting plates, due to quantum fluctuations of the electromagnetic (EM) field in the intervening space. {\it Thermal fluctuations} of correlated fluids (such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are also modified by the boundaries, resulting in finite-size corrections at criticality, and additional forces that effect wetting and layering phenomena. Modified fluctuations of the EM field can also account for the `van der Waals' interaction between conducting spheres, and have analogs in the fluctuation--induced interactions between inclusions on a membrane. We employ a path integral formalism to study these phenomena for boundaries of arbitrary shape. This allows us to examine the many unexpected phenomena of the dynamic Casimir effect due to moving boundaries. With the inclusion of quantum fluctuations, the EM vacuum behaves essentially as a complex fluid, and modifies the motion of objects through it. In particular, from the mechanical response function of the EM vacuum, we extract a plethora of interesting results, the most notable being: (i) The effective mass of a plate depends on its shape, and becomes anisotropic. (ii) There is dissipation and damping of the motion, again dependent upon shape and direction of motion, due to emission of photons. (iii) There is a continuous spectrum of resonant cavity modes that can be excited by the motion of the (neutral) boundaries.