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Wegner estimates and localization for continuum Anderson models with some singular distributions (1998)
| Content Provider | CiteSeerX |
|---|---|
| Author | Stollmann, Peter |
| Abstract | We give a simple geometric proof of Wegner's estimate which leads to a variety of new results on localization for multi--dimensional random operators. Introduction One of the most important topics in the mathematical theory of disordered solids is localization by which one understands the phenomenon that states are confined to a finite region in space. This is in sharp contrast to the case of ordered media where states travel to infinity and leave any finite region as time goes to infinity. Mathematically, localization is most commonly described by the occurence of pure point spectrum with exponentially decreasing eigenfunctions for the hamiltonian in question. For Anderson models, i.e. models of the form H(!) = H 0 + X i2\Gamma q i (!)f(\Delta \Gamma i) the general scheme of proof is by now quite well understood. Here e.g. H 0 = \Gamma\Delta +V 0 with \Gamma-periodic V 0 describes a medium with periodicity lattice \Gamma and the sum describes impurities by a random perturbation ... |
| File Format | |
| Volume Number | 75 |
| Journal | Arch. Math. (Basel |
| Language | English |
| Publisher Date | 1998-01-01 |
| Access Restriction | Open |
| Subject Keyword | Continuum Anderson Model Singular Distribution Wegner Estimate Finite Region Important Topic Delta Gamma New Result Sharp Contrast Periodicity Lattice Gamma Simple Geometric Proof Pure Point Spectrum Ordered Medium Multi Dimensional Random Operator Random Perturbation Anderson Model Disordered Solid Gamma Delta General Scheme Mathematical Theory I2 Gamma |
| Content Type | Text |
| Resource Type | Article |
