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Optimal Fluctuations and Tail States of non-Hermitian Operators

Francesca M. Marchetti·B. D. Simons
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Abstract

A statistical field theory is developed to explore the density of states and spatial profile of `tail states' at the edge of the spectral support of a general class of disordered non-Hermitian operators. These states, which are identified with symmetry broken, instanton field configurations of the theory, are closely related to localized sub-gap states recently identified in disordered superconductors. By focusing separately on the problems of a quantum particle propagating in a random imaginary scalar potential, and a random imaginary vector potential, we discuss the methodology of our approach and the universality of the results. Finally, we address potential physical applications of our findings.

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Francesca M. Marchetti, B. D. Simons. 2001-10-22. Optimal Fluctuations and Tail States of non-Hermitian Operators. https://doi.org/10.1088/0305-4470%2F34%2F49%2F305

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