Caught by Disorder: Bound States in Random Media
Disorder is one of the central topics in science today, and various aspects of the effects of disorder have changed a number of paradigms in mathematics and physics over the past 15 years. This work, the first treatment of the subject in book form, gives a hands-on introduction to disorder including a concise, mathematically rigorous examination of some particular models of disordered systems. The book presents a number of key unsolved problems and features many examples, illustrations, and an appendix containing the prerequisites of operator theory.
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Analysis of Andersontype Models
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absolutely continuous Anderson Localization Assume assumption band edges basic models boundary conditions bounded boxes called Cgeom compact consider defined denote disjoint disorder domain dynamical localization eigenfunction eigenvalues electrons energy ergodic exists exponential decay fact fixed fluctuation boundaries G G G H(co HA(co hamiltonian Hilbert space independent induction inequality initial length scale integrated density Kirsch kmax Lemma length scale estimates Let H Lifshitz tails linear Math mathematical measurable functions Moreover multiscale analysis norm Notes and Remarks open cube operator H perturbation Phys polynomially Preprint probability measure probability space properties prove pure point spectrum random models random operators random potential random Schrodinger operators random variables respect restriction Riesz Representation Theorem satisfied Schrodinger equation Section selfadjoint operator selfadjoint realization sequence sesquilinear form sidelength single-site measure single-site potential Sobolev space spectral theorem subspace theory tion waves Wegner estimate