Density of states in the non-hermitian Lloyd model

TL;DR

This paper examines the relationship between density of states and localization length in non-Hermitian quantum systems, highlighting the challenges in accurately determining the density of states for non-Hermitian Hamiltonians.

Contribution

It clarifies the connection between density of states and localization length and emphasizes the open problem of computing the density of states in non-Hermitian random Hamiltonians.

Findings

Localization length can be derived from the density of states in non-Hermitian systems.

Determining the density of states for non-Hermitian Hamiltonians remains an unresolved challenge.

Abstract

We reconsider the recently proposed connection between density of states in the so-called ``non-hermitian quantum mechanics'' and the localization length for a particle moving in random potential. We argue that it is indeed possible to find the localization length from the density of states of a non-hermitian random ``Hamiltonian''. However, finding the density of states of a non-hermitian random ``Hamiltonian'' remains an open problem, contrary to previous findings in the literature.