98-697 F. Klopp and L. Pastur

Lifshitz tails for random Schr{\"o}dinger operators with negative singular Poisson potential (510K, Gzipped Postscript) Nov 4, 98

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We develop a new method of asymptotic study of the integrated density of states $N(E)$ of a random Schr{\"o}dinger 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 allow 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.

Files: 98-697.src( 98-697.keywords , dpp.ps )