Non-Hermitean Localization and De-Localization

Details Non-Hermitean Localization and De-Localization Non-Hermitean Localization and De-Localization

1997-06-22

arxiv.org/abs/cond-mat/9706218v2

Phys.Rev. E59 (1999) 6433-6443

Physics

Condensed Matter

Disordered Systems and Neural Networks

35 pages, 4 ps figures, Latex. The revisions made are: note added to Section 3, a new section added concerning continuum "one

Scientific paper

10.1103/PhysRevE.59.6433

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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