Relativistic echo dynamics and the stability of a beam of Landau electrons

TL;DR

This paper extends echo dynamics and fidelity decay concepts to relativistic quantum mechanics, analyzing the stability of Landau electron beams under electromagnetic perturbations with a focus on Lorentz covariance.

Contribution

It introduces a covariant framework for echo dynamics in relativistic quantum systems and applies it to analyze Landau electron beam stability.

Findings

Fidelity expressions are derived for Klein-Gordon and Dirac equations.

Lorentz transformation properties of the echo operator are established.

The stability of Landau electron beams under field inhomogeneities is analyzed.

Abstract

We extend the concepts of echo dynamics and fidelity decay to relativistic quantum mechanics, specifically in the context of Klein-Gordon and Dirac equations under external electromagnetic fields. In both cases we define similar expressions for the fidelity amplitude under perturbations of these fields, and a covariant version of the echo operator. Transformation properties under the Lorentz group are established. An alternate expression for fidelity is given in the Dirac case in terms of a 4-current. As an application we study a beam of Landau electrons perturbed by field inhomogeneities.