Non-Hermitian localization and delocalization
Abstract
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.
- Publication:
-
Physical Review E
- Pub Date:
- June 1999
- DOI:
- 10.1103/PhysRevE.59.6433
- arXiv:
- arXiv:cond-mat/9706218
- Bibcode:
- 1999PhRvE..59.6433F
- Keywords:
-
- 02.50.-r;
- 05.20.-y;
- 11.10.-z;
- 71.20.-b;
- Probability theory stochastic processes and statistics;
- Classical statistical mechanics;
- Field theory;
- Electron density of states and band structure of crystalline solids;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Mesoscale and Nanoscale Physics
- E-Print:
- 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