Quantum work statistics of charged Dirac particles in time-dependent fields

TL;DR

This paper extends the quantum Jarzynski equality to relativistic quantum mechanics, providing exact work distributions for charged Dirac particles in time-dependent fields and highlighting relativistic subtleties.

Contribution

It introduces a framework for applying the Jarzynski equality to relativistic quantum systems and analytically solves for charged Dirac particles in dynamic fields.

Findings

Exact quantum work distributions for Dirac particles are derived.

The Jarzynski equality is verified in relativistic quantum contexts.

Relativistic effects introduce unique conceptual and technical challenges.

Abstract

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schr\"odinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.