A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide

TL;DR

This paper develops a path integral framework for classical and quantum dynamics using superspace, revealing new insights into entanglement and providing tools to compare classical and quantum evolution.

Contribution

It introduces a unified path integral approach for classical and quantum density matrix evolution, enabling analysis of entanglement and superoperator dynamics.

Findings

Path integrals for classical and quantum systems are formally identical.

The approach reveals distinctions between intra- and inter-space entanglement.

Perturbation theory for superoperator dynamics is developed.

Abstract

The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace (instead of Hilbert space), we describe time evolution of density matrices in terms of path integrals which are formally identical for quantum and classical mechanics. They only differ by the interaction contributing to the action. This allows to import tools developed for Feynman path integrals, in order to deal with superoperators instead of quantum mechanical commutators in real time evolution. Perturbation theory is derived. Besides applications in classical statistical physics, the "classical path integral" and the parallel study of classical and quantum evolution indicate new aspects of (dynamically assisted) entanglement (generation). Our findings suggest to distinguish 'intra'- from 'inter-space' entanglement.