Absence de spectre absolument continu pour un opérateur d'Anderson à potentiel d'interaction générique

Details Absence de spectre absolument continu pour un opérateur d'Anderson à potentiel d'interaction générique Absence de spectre absolument continu pour un opérateur d'Anderson à potentiel d'interaction générique

2010-02-18

arxiv.org/abs/1002.3440v1

Comptes Rendus de l Acad\'emie des Sciences - Series I - Mathematics 348, 3-4 (2010) p.175-179

Physics

Mathematical Physics

6 pages

Scientific paper

10.1016/j.crma.2010.01.03

We present a result of absence of absolutely continuous spectrum in an interval of $\R$, for a matrix-valued random Schr\"odinger operator, acting on $L^2(\R)\otimes \R^N$ for an arbitrary $N\geq 1$, and whose interaction potential is generic in the real symmetric matrices. For this purpose, we prove the existence of an interval of energies on which we have separability and positivity of the $N$ non-negative Lyapunov exponents of the operator. The method, based upon the formalism of F\"urstenberg and a result of Lie group theory due to Breuillard and Gelander, allows an explicit contruction of the wanted interval of energies.

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