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.
Keywords
random Schrödinger operators, sign-indefinite potentials,
Lifshitz tail