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Approach à la Borland to Multidimensional Localization

1985; American Physical Society; Volume: 55; Issue: 6 Linguagem: Inglês

10.1103/physrevlett.55.618

1092-0145

F. Delyon, Yves-Emmanuel Lévy, Bernard Souillard,

Numerical methods in inverse problems

We develop for the first time an approach \`a la Borland to Anderson localization in multidimensional systems; it provides a proof of localization when the Green's function decays exponentially, e.g., at large disorder or large energy. This approach also provides results about the Lyapunov exponents associated with a quasi-one-dimensional system. Finally we obtain the result that the singular continuous spectrum, found in some incommensurate systems, turns into exponential localization under arbitrarily small local perturbations.