Optimal Fluctuations and Tail States of non-Hermitian Operators

TL;DR

This paper introduces a variational method to analyze the rare tail states of non-Hermitian operators, refining existing instanton techniques, with applications demonstrated in quantum systems with imaginary potentials.

Contribution

It presents a new variational approach that improves the analysis of tail states in non-Hermitian operators, extending the instanton method.

Findings

Developed a general variational framework for tail state analysis.

Applied the method to quantum particles in imaginary potentials.

Enhanced understanding of spectral properties of non-Hermitian operators.

Abstract

We develop a general variational approach to study the statistical properties of the tail states of a wide class of non-Hermitian operators. The utility of the method, which is a refinement of the instanton approach introduced by Zittartz and Langer, is illustrated in detail by reference to the problem of a quantum particle propagating in an imaginary scalar potential.