Spectral Duality and Distribution of Exponents for Transfer Matrices of Block Tridiagonal Hamiltonians
نویسنده
چکیده
Abstract: The block-tridiagonal matrix structure is a common feature in Hamiltonians of models of transport. By allowing for a complex Bloch parameter in the boundary conditions, the Hamiltonian matrix and its transfer matrix are related by a spectral duality. As a consequence, I derive the distribution of the exponents of the transfer matrix in terms of the spectral density of the non-Hermitian Hamiltonian: this formula is the single-matrix analogue of the Herbert-Jones-Thouless formula, for the case of many Lyapunov exponents. I also discuss some implications of duality on the distribution (real bands and complex arcs) and the dynamics of energy eigenvalues. P.A.C.S.: 02.10.Yn (matrix theory), 72.15.Rn (localization effects), 72.20.Ee (mobility edges, hopping transport)
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