Osaka Journal of Mathematics

Wegner estimate and localization for random magnetic fields

Naomasa Ueki

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Abstract

Inspired by a work of Hislop and Klopp, we prove precise Wegner estimates for three classes of Schrödinger operators, including Pauli Hamiltonians, with random magnetic fields. The support of the site vector potentials may be noncompact (long-range type random perturbation) and, for one class of the operators, the random vector potentials may be unbounded. In particular Gaussian random fields are also treated. Wegner estimates with correct volume dependence are applied to show Hölder estimates of the densities of states. We give also upper bounds on the infimum of the spectrum to show the existence of the Anderson localization near the infimum.

Article information

Source
Osaka J. Math., Volume 45, Number 3 (2008), 565-608.

Dates
First available in Project Euclid: 17 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1221656642

Mathematical Reviews number (MathSciNet)
MR2468583

Zentralblatt MATH identifier
1153.82009

Subjects
Primary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 47B80: Random operators [See also 47H40, 60H25] 47N55 60H25: Random operators and equations [See also 47B80] 82B05: Classical equilibrium statistical mechanics (general)

Citation

Ueki, Naomasa. Wegner estimate and localization for random magnetic fields. Osaka J. Math. 45 (2008), no. 3, 565--608. https://projecteuclid.org/euclid.ojm/1221656642


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