منابع مشابه
Anderson Localization and Lifshits Tails for Random Surface Potentials
We consider Schrödinger operators on L2(Rd) with a random potential concentrated near the surface Rd1 ×{0} ⊂ Rd. We prove that the integrated density of states of such operators exhibits Lifshits tails near the bottom of the spectrum. From this and the multiscale analysis by Boutet de Monvel and Stollmann [Arch. Math. 80 (2003) 87] we infer Anderson localization (pure point spectrum and dynamic...
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We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ as N → ∞ in the subcritical regime 0 < p < 1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of ∆ exhibits a Lifshits-tail behaviour at the lower spectr...
متن کاملThe Fate of Lifshits Tails in Magnetic Fields
We investigate the integrated density of states of the Schrr odinger operator in the Euclidean plane with a perpendicular constant magnetic eld and a random potential. For a Poisson random potential with a non-negative algebraically decaying single-impurity potential we prove that the leading asymptotic behaviour for small energies is always given by the corresponding classical result in contra...
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ژورنال
عنوان ژورنال: Annales Henri Poincaré
سال: 2018
ISSN: 1424-0637,1424-0661
DOI: 10.1007/s00023-018-0680-8