Positivit\'e des exposants de Lyapounov pour un op\'erateur de Schr\"odinger continu \`a valeurs matricielles

Abstract

In this note, we study a continuous matrix-valued Anderson-type model. Both leading Lyapounov exponents of this model are proved to be positive and distincts for all energies in $(2,+\infty)$ except those in a discrete set, which leads to absence of absolutely continuous spectrum in $(2,+\infty)$. The methods, using group theory results by Breuillard and Gelander, allow for singular Bernoulli distributions.