Optimal Fluctuations and Tail States of non-Hermitian Operators

Details Optimal Fluctuations and Tail States of non-Hermitian Operators Optimal Fluctuations and Tail States of non-Hermitian Operators

2001-10-22

arxiv.org/abs/cond-mat/0110467v1

J. Phys. A: Math. Gen. 34 (2001) 10805-10828

Physics

Condensed Matter

Disordered Systems and Neural Networks

27 pages AMSLaTeX (with LaTeX2e), 12 eps figures (J. Phys. A, to appear)

Scientific paper

10.1088/0305-4470/34/49/305

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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