A Non-Hermitean Particle in a Disordered World

TL;DR

This paper explores the spectral properties of non-Hermitian Hamiltonians in disordered systems, providing new results for higher dimensions and an approximate spectrum expression using WKB methods.

Contribution

It introduces new findings on the spectrum of non-Hermitian Hamiltonians in higher spatial dimensions and derives an approximate spectral expression via WKB approximation.

Findings

New spectral results in higher dimensions

WKB approximation for spectrum

Insights into vortex line pinning physics

Abstract

There has been much recent work on the spectrum of the random non-hermitean Hamiltonian which models the physics of vortex line pinning in superconductors. This note is loosely based on the talk I gave at the conference "New Directions in Statistical Physics" held in Taipei, August 1997. We describe here new results in spatial dimensions higher than one. We also give an expression for the spectrum within the WKB approximation.