Non-Hermitian spectra and Anderson localization

Abstract

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.

8 pages, 10 figures

References in corpus (3)

• Weak disorder expansion for localization lengths of quasi-1D systems
• Spectral duality and distribution of exponents for transfer matrices of block tridiagonal Hamiltonians
• Boundary hopping and the mobility edge in the Anderson model in three dimensions

Cited by in corpus (1)

• Spectral Curves and Localization in Random Non-Hermitian Tridiagonal Matrices