Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at short distances. We calculate the joint probability of complex eigenvalues and some other correlation functions. We find that the transition is abrupt and it is due to an interplay between two saddle points in the free energy functional.
Physical Review Letters
- Pub Date:
- June 2000
- Condensed Matter - Disordered Systems and Neural Networks;
- High Energy Physics - Lattice;
- High Energy Physics - Theory
- 4 pages, 1 figure