Relativistic Lindblad description of the electron's radiative dynamics

TL;DR

This paper introduces a relativistic open quantum system model for electron radiation dynamics, integrating quantum effects like vacuum fluctuations and Zitterbewegung, and connects quantum and classical descriptions of radiation reaction.

Contribution

It develops a relativistic Lindblad master equation framework that incorporates quantum vacuum effects into electron radiation dynamics, bridging quantum and classical models.

Findings

Captures quantum vacuum fluctuations in the Landau-Lifshitz equation.

Reveals the quantum origin of electron Zitterbewegung.

Provides a phase-space and semiclassical analysis of relativistic electron dynamics.

Abstract

An effective model for describing the relativistic quantum dynamics of a radiating electron is developed via a relativistic generalization of the Lindblad master equation. By incorporating both radiation reaction and vacuum fluctuations into the Dirac equation within an open quantum system framework, our approach captures the Zitterbewegung of the electron, ensuing noncommutativity of its effective spatial coordinates, and provides the quantum analogue of the Landau-Lifshitz (LL) classical equation of motion with radiation reaction. We develop the corresponding phase-space representation via the relativistic Wigner function and derive the semiclassical limit through a Foldy-Wouthuysen transformation. The latter elucidates the signature of quantum vacuum fluctuations in the LL equation, and shows its relationship with the corrected Sokolov equation. Our results offer a robust framework for investigating quantum radiation reaction effects in ultrastrong laser fields.