Ehrenfest+R Dynamics I: A Mixed Quantum-Classical Electrodynamics Simulation of Spontaneous Emission

TL;DR

This paper introduces Ehrenfest+R dynamics, a novel mixed quantum-classical simulation method that accurately models spontaneous emission by explicitly including electron-photon interactions and overcoming limitations of traditional Ehrenfest dynamics.

Contribution

The paper develops Ehrenfest+R dynamics, enhancing mixed quantum-classical simulations to correctly reproduce spontaneous emission and distinguish electromagnetic phenomena.

Findings

Ehrenfest+R accurately models spontaneous emission.

The method distinguishes electromagnetic fluctuations from coherent emission.

It improves upon traditional Ehrenfest dynamics in quantum-electrodynamics simulations.

Abstract

The dynamics of an electronic system interacting with an electromagnetic field is investigated within mixed quantum-classical theory. Beyond the classical path approximation (where we ignore all feedback from the electronic system on the photon field), we consider all electron-photon interactions explicitly according to Ehrenfest (i.e. mean-field) dynamics and a set of coupled Maxwell-Liouville equations. Because Ehrenfest dynamics cannot capture certain quantum features of the photon field correctly, we propose a new Ehrenfest+R method that can recover (by construction) spontaneous emission while also distinguishing between electromagnetic fluctuations and coherent emission.