Full spectrum Anderson localization for a general model of a disordered quantum wire

Mathematicians have long been interted in rigorously understanding the conductivity properties of disordered materials at the quantum level, in particular after the work of the Nobel Prize winning American physicist Philip W. Anderson (1923-2020)

In 1990, Klein, Lacroix and Speis analyzed a well studied random operator model for an electron moving on a portion of lattice of the form Z × [0, W], W ? N and subject to a random potential, called Anderson model on the strip. They showed, in particular, that such a model boasts spectral localization on all of its energy spectrum, a well defined mathematical property that is a very powerful signature of the electron getting trapped in a region by the potential.

In thie present work, we focus on a more general model of a quantum particle with internal degrees of freedom moving in a quasi 1D random medium (disordered quantum wire), that we call "generalized Wegner Orbital Model".

In particular, we prove spectral and dynamical localization at all energies for such a model suggesting that the disordered materials belonging to the wide class described by this model are all perfect insulators.

In this talk, I will start by introducing basic concepts related to Anderson Localization in general, then move to the specific model considered in this work, and outline our proof of its spectral localization. The proof combines techniques from probability theory, spectral theory of selfadjoint operator and ergodic theory, with an unexpected algebraic twist...