Lifshitz tails for random Schrödinger operators with negative singular Poisson potential. (English) Zbl 0937.60098

Klopp, Frédéric; Pastur, Leonid

Commun. Math. Phys. 206, No. 1, 57-103 (1999).

Summary: 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 \(E\to-\infty\) for the Poisson random potential with a singular single-site (impurity) potential, in particular, for the screened Coulomb impurities, dislocations, etc.

MSC:

60K40	Other physical applications of random processes
82B44	Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics

Keywords:

random Schrödinger operator; Dirichlet-Neumann bracketing; Poisson random potential; screened Coulomb impurities