Feynman Diagrams for Dispersion Interactions Out of Equilibrium -- Two-Body Potentials for Atoms with Initial Excitation

TL;DR

This paper reviews diagrammatic techniques for calculating non-equilibrium dispersion forces between atoms, emphasizing the role of decay processes and excited states in biological and physical systems.

Contribution

It introduces a full non-equilibrium theoretical framework for dispersion interactions involving excited atoms, clarifying previous mathematical ambiguities.

Findings

Decay processes significantly influence intermolecular potentials.

Excited states can lead to resonant forces affecting biological reactions.

Non-equilibrium diagrams simplify calculations of complex interactions.

Abstract

Diagrammatic techniques are well-known in the calculation of dispersion interactions between atoms or molecules. The multipolar coupling scheme combined with Feynman ordered diagrams significantly reduces the number of graphs compared to elementary stationary perturbation theory. We review calculations of van der Waals-Casimir-Polder forces, focusing on two atoms or molecules one of which is excited. In this case, calculations of the corresponding force are notorious for mathematical issues connected to the spontaneous decay of the excitation. Treating such unstable states in a full non-equilibrium theory provides a physical interpretation of apparent contradictions in previous results and underlines the importance of decay processes for the intermolecular potential. This may have important implications on reactions in biological systems, where excited states may be relatively long-lived and the resonant intermolecular force may result in directed Brownian motion.