Séminaire Orléans
The long-range Anderson model with weakly decaying off-diagonal termsConstanza Rojas-Molina (Cergy)
Thursday 12 December 2024 14:00 - Orléans - Salle de Séminaires
Résumé :
The Anderson model is a random Schrödinger operator used in the study of the properties of materials with impurities. The dynamics of a particule propagating in such material is governed by the Schrödinger equation driven by a Schrödinger operator that is a random perturbation of the Laplacian. The randomness in the material typically suppresses the propagation of quantum waves, a phenomenon called Anderson Localization. In this talk we will review results on the localization properties of long-range Anderson models in the discrete setting, where the Laplacian is replaced by a non-local operator. This includes the fractional Anderson model, a long-range operator with weakly polynomially decaying off-diagonal terms, and diagonal randomness. We discuss the effects of non-locality on the spectral and dynamical properties of the system. The interest in these models lies in their association to stable Levy processes, random walks with long jumps and anomalous diffusion.
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