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Lifshits tails caused by anisotropic decay: the emergence of a quantum-classical regime. (English) Zbl 1093.82011

In this paper the authors investigate the Lifshits-tail behaviour of the integrated density of states for some classes of Schrödinger operators with positive random potentials. They consider both the case of potentials that decay in an anisotropic way at infinity and the class of random potentials given in terms of random Borel measures.

MSC:

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
35J10 Schrödinger operator, Schrödinger equation
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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