Browsing by Author "Sadel, Christian"

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    Absolutely continuous spectrum for Schrodinger operators with random decaying matrix potentials on the strip
    (2023) Gonzalez Aguirre, Hernán Felipe; Sadel, Christian
    We consider a family of random Schrödinger operators on the discrete strip with decaying random matrix potential. We prove that the spectrum is almost surely pure absolutely continuous, apart from random, possibly embedded, eigenvalues which may accumulate at band edges.
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    Footprint of a topological phase transition on the density of states
    (2023) De Moor, Joris; Sadel, Christian; Schulz-Baldes, Hermann
    For a generalized Su–Schrieffer–Heeger model, the energy zero is always critical and hyperbolic in the sense that all reduced transfer matrices commute and have their spectrumofftheunitcircle.Disorder-driventopologicalphasetransitionsinthismodel are characterized by a vanishing Lyapunov exponent at the critical energy. It is shown that away from such a transition the density of states vanishes at zero energy with an explicitly computable Hölder exponent, while it has a characteristic divergence (Dyson spike) at the transition points. The proof is based on renewal theory for the Prüfer phase dynamics and the optional stopping theorem for martingales of suitably constructed comparison processes.
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    On absolutely continuous spectrum for one-channel unitary operators
    (2024) Bourget, Olivier; Moreno, Gregorio; Sadel, Christian; Taarabt, Amal
    In this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog of Carmona's formula and deduce criteria for absolutely continuous spectrum which we apply to random Hilbert Schmidt perturbations of periodic scattering zippers.