Optimal Fluctuations and Tail States 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.

4 pages, 2 figures, to appear in PRL

References in corpus (5)

• Eigenvector statistics in non-Hermitian random matrix ensembles
• Random Dirac Fermions and Non-Hermitian Quantum Mechanics
• Delocalization in an open one-dimensional chain in an imaginary vector potential
• Quantum Mechanics with Random Imaginary Scalar Potential
• Finite Size Effects in Vortex Localization

Cited by in corpus (7)

• Random Matrices close to Hermitian or unitary: overview of methods and results
• Light Localization induced by Random Imaginary Permittivities
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices
• Lifshitz tail states in non-Hermitian disordered photonic lattices
• "Lifshitz tails" and extended states in an Imaginary random potential
• Optimal Fluctuations and Tail States of non-Hermitian Operators