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Non-Hermitean Localization and De-Localization

Joshua Feinberg·A. Zee
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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.

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Joshua Feinberg, A. Zee. 1997-08-29. Non-Hermitean Localization and De-Localization. https://doi.org/10.1103/physreve.59.6433

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