Abstract
I review some recent results on Schrödinger equations with random potentials, and specially discuss the known examples where a transition in the nature of the spectrum occurs when varying the coupling constant or the energy: a transition from pure point spectrum with power decaying eigenfunctions to purely continuous spectrum has been proven recently for two classes of disordered systems, a transition which differs from the Mott-Anderson transition proven in certain Anderson models.
I will also discuss relevance of localization theory to hydrodynamics and plasma physics.
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Souillard, B. (1985). Transition from Pure Point to Continuous Spectrum for Random Schrödinger Equations: Some Examples. In: Fritz, J., Jaffe, A., Szász, D. (eds) Statistical Physics and Dynamical Systems. Progress in Physics, vol 10. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-6653-7_23
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DOI: https://doi.org/10.1007/978-1-4899-6653-7_23
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