Lifshitz Tails for Generalized Alloy Type Random Schrödinger Operators

Frédéric Klopp (1) , Shu Nakamura (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Graduate School of Mathematical Sciences

We study Lifshitz tails for random Schrödinger operators where the random potential is alloy type in the sense that the single site potentials are independent, identically distributed, but they may have various function forms. We suppose the single site potentials are distributed in a finite set of functions, and we show that under suitable symmetry conditions, they have Lifshitz tail at the bottom of the spectrum except for special cases. When the single site potential is symmetric with respect to all the axes, we give a necessary and sufficient condition for the existence of Lifshitz tails. As an application, we show that certain random displacement models have Lifshitz singularity at the bottom of the spectrum, and also complete the study of continuous Anderson type models undertaken in arXiv : 0804.4079

Mots clés: Lifshitz tails; non monotonous operators; Dirichlet-to-Neuman operator

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Frédéric Klopp, Shu Nakamura. Lifshitz Tails for Generalized Alloy Type Random Schrödinger Operators. 2009. ⟨hal-00367638v3⟩