Quantum field theory of the van der Waals friction

TL;DR

This paper develops a quantum field theoretical approach to calculate van der Waals friction between solids and particles, aligning with Lifshitz theory, and suggests it can be experimentally measured with current technology.

Contribution

It introduces a quantum field theory framework for van der Waals friction that can handle complex geometries and matches existing Lifshitz-based calculations.

Findings

The approach agrees with Lifshitz theory calculations.

Van der Waals friction can be measured with current experimental setups.

The method is extendable to bodies with complex geometries.

Abstract

The van der Waals friction between two semi-infinite solids, and between a small neutral particle and semi-infinite solid is reconsidered on the basis of thermal quantum field theory in the Matsubara formulation. The calculation of the friction to linear order in the sliding velocity is reduced to the finding of the equilibrium Green functions. Thus this approach cab be extended for bodsies with complex geometry. The friction calculated in this approach agrees with the friction calculated using a dynamical modification of the Lifshitz theory, which is based on the fluctuation-dissipation therem. We show that the van der Waals fricxtion can be measured in non-contact friction experiment using state-of-the art equipment.