Non-Hermitean Localization and De-Localization

Abstract

We study localization and delocalization in a class of non-hermitean Hamiltonians inspired by the problem of vortex pinning in superconductors. In various simplified models we are able to obtain analytic descriptions, in particular of the non-perturbative emergence of a forked structure (the appearance of "wings") in the density of states. We calculate how the localization length diverges at the localization-delocalization transition. We map some versions of this problem onto a random walker problem in two dimensions. For a certain model, we find an intricate structure in its density of states.

35 pages, 4 ps figures, Latex. The revisions made are: note added to Section 3, a new section added concerning continuum "one way" models, minor corrections made and comments added to section 6, references added and updated

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