Absence of absolutely continuous spectrum for random scattering zippers

A scattering zipper is a system obtained by concatenation of scattering events with equal even number of incoming and outgoing channels. The associated scattering zipper operator is the unitary analog of Jacobi matrices with matrix entries. For infinite identical events and independent and identical...

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Bibliographic Details
Published in:Journal of mathematical physics 2015-02, Vol.56 (2), p.1
Main Authors: Boumaza, Hakim, Marin, Laurent
Format: Article
Language:English
Subjects:
Dynamical Systems
Liapunov exponents
Mathematical Physics
Mathematics
Matrix
Operators (mathematics)
Physics
Scattering
Spectral Theory
Zippers
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Summary:A scattering zipper is a system obtained by concatenation of scattering events with equal even number of incoming and outgoing channels. The associated scattering zipper operator is the unitary analog of Jacobi matrices with matrix entries. For infinite identical events and independent and identically distributed random phases, Lyapunov exponents positivity is proved and yields absence of absolutely continuous spectrum by Kotani’s theory.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4906809