Random Dirac Fermions and Non-Hermitian Quantum Mechanics

TL;DR

This paper explores how a strong imaginary vector potential affects two-dimensional quantum particles in a random potential, linking non-Hermitian operators to Dirac equations with random gauge fields, and discussing implications for localization and critical states.

Contribution

It establishes a novel connection between non-Hermitian quantum mechanics and Dirac equations with random gauge fields in two dimensions, advancing understanding of localization phenomena.

Findings

Wavefunctions of non-Hermitian operators relate to 2D Dirac equations with random gauge fields.

Impacts on localization properties and critical states are analyzed.

Provides a framework for studying non-Hermitian quantum systems in disordered environments.

Abstract

We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian operator can be obtained as the solution to a two-dimensional Dirac equation in the presence of a random gauge field. Consequences for the localization properties and the critical nature of the states are discussed.