Relativistic electron wave packets featuring persistent quantum backflow

TL;DR

This paper presents exact solutions to Dirac's equation in a cylindrical waveguide, revealing stable, persistent quantum backflow phenomena that become spin-polarized in the nonrelativistic limit, regardless of initial conditions.

Contribution

It provides closed-form relativistic wave packet solutions demonstrating persistent quantum backflow in a cylindrical waveguide, a novel insight into relativistic quantum dynamics.

Findings

Quantum backflow occurs at almost any distance along the waveguide.

Backflow solutions are stable over time.

Wave packets become spin-polarized in the nonrelativistic limit.

Abstract

Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a cross-section of the cylinder at practically any distance along the waveguide, becoming spin-polarized in the nonrelativistic limit. The predicted backflow is stable in time and is manifest regardless of the initial wave function.