Absence of absolutely continuous spectrum for random scattering zippers
Laurent
Marin
lrnt.marin@gmail.com
GDR DYNQUA.
2013-03-12
[
](paper.doc)
11 pages.
Absence of absolutely continuous spectrum for random scattering zippers
Laurent
Marin
lrnt.marin@gmail.com
Lyapunov exponents
random operators
scattering zippers
Kotani theory
34D08, 34L40, 34L05, 47B80, 82B44
A scattering zipper is a system obtained by concatenation of scattering events with equal even number of incoming and out going channels. The associated scattering zipper operator is the unitary equivalent of Jacobi matrices with matrix entries. For infinite identical events and random phases, Lyapunov exponents positivity is proved and yields to the absence of absolutely continuous spectrum.