Localization in non-Hermitian quantum mechanics and flux-line pinning in superconductors

TL;DR

This paper reviews recent advances in non-Hermitian quantum systems, highlighting how large imaginary vector potentials induce delocalization, with applications to flux-line depinning in superconductors, supported by analytical and numerical analysis.

Contribution

It introduces the connection between non-Hermitian quantum mechanics and flux-line pinning, providing new insights into delocalization phenomena in disordered systems.

Findings

Delocalization occurs in 1D and 2D with large imaginary potentials.

The delocalization transition relates to the complex energy spectrum.

Numerical and analytical results support the theoretical framework.

Abstract

A recent development in studies of random non-Hermitian quantum systems is reviewed. Delocalization was found to occur under a sufficiently large constant imaginary vector potential even in one and two dimensions. The phenomenon has a physical realization as flux-line depinning in type-II superconductors. Relations between the delocalization transition and the complex energy spectrum of the non-Hermitian systems are described. Analytical and numerical results obtained for a non-Hermitian Anderson model are shown.