Non-Hermitian localization and delocalization.
We study localization and delocalization in a class of non-Hermitian 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 nonperturbative 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.
Feinberg
J
J
Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA. joshua@physics.technion.ac.il
Zee
A
A