Caught by Disorder: Bound States in Random MediaSpringer Science & Business Media, 2001 - 166 Seiten Introduction * 1. Getting Started * 1.1. Bound States versus Extended States * 1.2. Ergodic Operator Families * 1.3. Some Important Examples * 1.4. Our Basic Models (P + A) and (DIV) * 1.5. Localization and Lifshitz Tails: The Heuristic Picture * 2. Analysis of Anderson-type Models * 2.1. Lifshitz Tails for (P + A) * 2.2. Initial Length Scale Estimates * 2.3. Wegner Estimates * 2.4. Combes--Thomas Estimates * 2.5. Changing Cubes * 3. Multiscale Analysis * 3.1. Idea of the Proof of Localization and Historical Notes * 3.2. Multiscale Analysis * 3.3. Exponential Localization * 3.4. Dynamical Localization * 3.5. More Models * 4. Appendix * 4.1. A Short Story of Selfadjoint Operators * 4.2. Some Basics from Probability Theory * 5. Aftermath * References * Index |
Inhalt
Getting Started | v |
Analysis of Andersontype Models | 23 |
Multiscale Analysis | 55 |
Appendix | 97 |
Aftermath | 131 |
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Häufige Begriffe und Wortgruppen
absolutely continuous AL(x Anderson Localization Assume band edges basic models boundary conditions bounded boxes Cgeom compact consider defined denote disjoint disorder domain dynamical localization E)-good eigenfunction eigenvalues energy ergodic exists exponential decay fact fluctuation boundaries HA(w hamiltonian Hilbert space Hölder continuous independent induction inequality initial length scale integrated density Kirsch L²(A L²(Rd Lemma length scale estimates Let H Lifshitz tails linear Math mathematical Moreover multiscale analysis norm Notes and Remarks open cube operator H perturbation Phys polynomially probability space properties prove pure point spectrum random operators random potential random Schrödinger operators respect restriction Riesz Representation Theorem satisfied Schrödinger equation Schrödinger operators Section selfadjoint operator selfadjoint realization sequence sesquilinear form single-site measure single-site potential Sobolev space Spectral Theorem spectrum of H Stollmann subspace theory tion waves Wegner estimate
Beliebte Passagen
Seite 151 - Lifschitz tail in a magnetic field: coexistence of classical and quantum behavior in the borderline case. Probab. Theory Related Fields, 121(2):219-236, 2001.