Absence of absolutely continuous spectrum for an Anderson-Bernoulli operator with generic interaction potential

作者：Boumaza Hakim^*

来源：Comptes Rendus Mathematique, 2010, 348(3-4): 175-179.

DOI：10.1016/j.crma.2010.01.031

We present a result of absence of absolutely continuous spectrum in an interval of R, for a matrix-valued random Schrodinger operator, acting on L(2)(R) circle times R(N) for an arbitrary N >= 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 Furstenberg and a result of Lie group theory due to Breuillard and Gelander, allows an explicit construction of the wanted interval of energies.

• 出版日期2010-2