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Reidemeister torsion of a symplectic complex
Get PDFWe consider a claim mentioned in [33] p.187 about the relation between a symplectic chain complex with !-compatible bases and Reidemeister Torsion of it. This is an explanation of it
Wegner estimate and localization for random magnetic fields
Get PDFInspired 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
