NonHermitian Anderson model: Lyapunov exponents, eigenvalues, and eigenfunctions
NonHermitian Anderson model: Lyapunov exponents, eigenvalues, and eigenfunctions

Ilya Goldsheid, Queen Mary, University of London
Jadwin Hall 343
The NonHermitian Anderson model was introduce in 1996 by N. Hatano and D. Nelson. Their numerical studies reveled very interesting and unusual spectral properties of this model. The aim of my talk is to explain how the theory of Lyapunov exponents allows one to: (a) obtain the equations for the curves on which the nonreal eigenvalues lie (b) study the unusually regular behavior of these eigenvalues (c) show that the eigenfunctions corresponding to the nonreal eigenvalues are $exp(\sqrt{n})$localized in a finite box of size $N$ but become delocalized as $N\rightarrow \infty$.