Non-Hermitian Anderson model: Lyapunov exponents, eigenvalues, and eigenfunctions

Non-Hermitian Anderson model: Lyapunov exponents, eigenvalues, and eigenfunctions

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Ilya Goldsheid, Queen Mary, University of London
Jadwin Hall 343

The Non-Hermitian 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 non-real eigenvalues lie (b) study the unusually regular behavior of these eigenvalues (c) show that the eigenfunctions corresponding to the non-real eigenvalues are $exp(-\sqrt{n})$-localized in a finite box of size $N$ but become de-localized as $N\rightarrow \infty$.