Abstract
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 a 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 a Lifshitz singularity at the bottom of the spectrum, and also complete our previous study (2009) of continuous Anderson type models.
Citation
Frédéric Klopp. Shu Nakamura. "Lifshitz tails for generalized alloy-type random Schrödinger operators." Anal. PDE 3 (4) 409 - 426, 2010. https://doi.org/10.2140/apde.2010.3.409
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