Massless Dirac particle in a stochastic magnetic field: A solvable quantum walk approximation

TL;DR

This paper models a massless Dirac particle in a stochastic magnetic field as a quantum walk with noise, revealing a transition from ballistic to diffusive motion, with potential implications for solar neutrino fluxes.

Contribution

It introduces an exactly solvable quantum walk approximation for a Dirac particle in a stochastic magnetic field, linking quantum dynamics to classical diffusion.

Findings

Motion transitions from ballistic to diffusive over time

Exact solution for the quantum walk with unitary noise

Potential relevance to solar neutrino fluxes

Abstract

A massless Dirac particle is considered, moving along the x-axis while Pauli-coupled by its anomalous magnetic moment to a piecewise constant magnetic field along the same axis, with stochastically varying sign. The motion is approximated as a quantum walk with unitary noise, for which the evolution can be found exactly. Initially ballistic, the motion approaches a classical diffusion on a time-scale determined by the speed of light, the size of the magnetic moment, the strength of the field and the time interval between changes in its direction. It is suggested that a process of this type could occur in the Sun's corona, significantly affecting the solar fluxes of one or more neutrino types.