Data di Pubblicazione:
2011
Citazione:
Counting the exponents of single transfer matrices / L.G. Molinari, G. Lacagnina. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 52:6(2011), pp. 063501.063501.1-063501.063501.8.
Abstract:
The eigenvalue equation of a band or a block tridiagonal matrix, the tight binding model for a crystal, a molecule, or a particle in a
lattice with random potential or hopping amplitudes: these and other problems lead to three-term recursive relations for (multicomponent) amplitudes. Amplitudes $n$ steps apart are linearly related by a transfer matrix, which is the product of $n$ matrices. Its exponents describe the decay lengths of the amplitudes. A formula is obtained for the counting function of the exponents, based on a duality relation and the Argument Principle for the zeros of
analytic functions. It involves the corner blocks of the inverse of the associated
Hamiltonian matrix. As an illustration, numerical evaluations of the counting function of quasi 1D Anderson model are shown.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Lyapunov spectrum ; Anderson localization ; transfer matrix ; block tridiagonal matrix
Elenco autori:
L.G. Molinari, G. Lacagnina
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