Non-Hermitian localization and delocalization

We study localization and delocalization in a class of non-Hermitian Hamilt onians inspired by the problem of vortex pinning in superconductors. In var ious simplified models we are able to obtain analytic descriptions, in part icular, of the nonperturbative emergence of a forked structure (the appeara nce 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. F or a certain model, we find an intricate structure in its density of states . [S1063-651X(99)05406-9].