IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 42 (2009) 265204 (15pp) doi: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 into non-Hermitian spectra of Anderson’s model in D = 1, 2 and into the smallest exponent is presented. PACS numbers: 71.23.An, 02.20.−a 1