Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 42, Issue 26, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/42/26/265204
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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 into non-Hermitian spectra of Anderson's model in D = 1, 2 and into the smallest exponent is presented.
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