Non-Hermitian spectra and Anderson localization

Details Non-Hermitian spectra and Anderson localization Non-Hermitian spectra and Anderson localization

2008-08-08

arxiv.org/abs/0808.1241v2

J. Phys. A: Math. Theor. 42 (2009) 265204 (15pp.)

Physics

Mathematical Physics

8 pages, 10 figures

Scientific paper

10.1088/1751-8113/42/26/265204

The spectrum of exponents of the transfer matrix provides the localization lengths of Anderson's model for a particle in a lattice with disordered potential. I show that a duality identity for determinants and Jensen's identity for subharmonic functions, give a formula for the spectrum in terms of eigenvalues of the Hamiltonian with non-Hermitian boundary conditions. The formula is exact; it involves an average over a Bloch phase, rather than disorder. A preliminary investigation of non-Hermitian spectra of Anderson's model in D=1,2 and on the smallest exponent is presented.

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