Ballistic transport in random magnetic fields with anisotropic long-ranged correlations

TL;DR

This paper provides exact theoretical insights into the transport properties of a spinless charged quantum particle in a 2D plane under a anisotropic, long-range correlated random magnetic field, extending previous foundational results.

Contribution

It introduces a solvable model for quantum transport in anisotropic, long-range correlated magnetic fields, generalizing earlier isotropic cases and offering new analytical results.

Findings

Exact solutions for energetic and dynamic properties

Extension of Iwatsuka and Müller models to anisotropic fields

Insights into transport in quasi-2D semiconductor structures

Abstract

We present exact theoretical results about energetic and dynamic properties of a spinless charged quantum particle on the Euclidean plane subjected to a perpendicular random magnetic field of Gaussian type with non-zero mean. Our results refer to the simplifying but remarkably illuminating limiting case of an infinite correlation length along one direction and a finite but strictly positive correlation length along the perpendicular direction in the plane. They are therefore ``random analogs'' of results first obtained by A. Iwatsuka in 1985 and by J. E. M\"uller in 1992, which are greatly esteemed, in particular for providing a basic understanding of transport properties in certain quasi-two-dimensional semiconductor heterostructures subjected to non-random inhomogeneous magnetic fields.