Localization transitions in non-Hermitian quantum mechanics

TL;DR

This paper investigates localization transitions in non-Hermitian quantum systems with imaginary vector potentials, linking them to flux line depinning in superconductors, and predicts associated physical phenomena like the transverse Meissner effect.

Contribution

It introduces a path-integral approach to analyze localization transitions in non-Hermitian quantum mechanics and relates these to flux line depinning in superconductors.

Findings

Prediction of stretched exponential relaxation of magnetic fields.

Diverging penetration depth at the transition point.

Connection between quantum localization and superconductor flux dynamics.

Abstract

We study the localization transitions which arise in both one and two dimensions when quantum mechanical particles described by a random Schr\"odinger equation are subjected to a constant imaginary vector potential. A path-integral formulation relates the transition to flux lines depinned from columnar defects by a transverse magnetic field in superconductors. The theory predicts that the transverse Meissner effect is accompanied by stretched exponential relaxation of the field into the bulk and a diverging penetration depth at the transition.