Absence of absolutely continuous spectrum for random scattering zippers

Hakim Boumaza (1) , Laurent Marin (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 IF - Institut Fourier

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.

Mots clés: Lyapunov exponents; random operators; scattering zippers; Kotani theory

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Systèmes dynamiques [math.DS]

Hakim Boumaza, Laurent Marin. Absence of absolutely continuous spectrum for random scattering zippers. Journal of Mathematical Physics, 2015, 56 (2). ⟨hal-00800028⟩