Lifshitz Tails for Random Schrödinger Operators¶with Negative Singular Poisson Potential

Abstract:

We develop a method of asymptotic study of the integrated density of states (IDS) N(E) of a random Schrödinger operator with a non-positive (attractive) Poisson potential. The method is based on the periodic approximations of the potential instead of the Dirichlet-Neumann bracketing used before. This allows us to derive more precise bounds for the rate of approximations of the IDS by the IDS of respective periodic operators and to obtain rigorously for the first time the leading term of log N(E) as E→−∞ for the Poisson random potential with a singular single-site (impurity) potential, in particular, for the screened Coulomb impurities, dislocations, etc.