On the Wegner orbital model

Abstract

The Wegner orbital model is a class of random operators introduced by Wegner to model the motion of a quantum particle with many internal degrees of freedom (orbitals) in a disordered medium. We consider the case when the matrix potential is Gaussian, and prove three results: localisation at strong disorder, a Wegner-type estimate on the mean density of eigenvalues, and a Minami-type estimate on the probability of having multiple eigenvalues in a short interval. The last two results are proved in the more general setting of deformed block-Gaussian matrices, which includes a class of Gaussian band matrices as a special case. Emphasis is placed on the dependence of the bounds on the number of orbitals. As an additional application, we improve the upper bound on the localisation length for one-dimensional Gaussian band matrices.

23 pages

References in corpus (5)

• Generalized eigenvalue-counting estimates for the Anderson model
• Density of States for Random Band Matrices in two dimensions
• Matrix regularizing effects of Gaussian perturbations
• Transfer matrix approach to 1d random band matrices: density of states
• How large is large? Estimating the critical disorder for the Anderson model

Cited by in corpus (7)

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• The effective potential of an $M$-matrix
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• On the local eigenvalue statistics for random band matrices in the localization regime
• Delocalization and continuous spectrum for ultrametric random operators
• Manifolds pinned by a high-dimensional random landscape: Hessian at the global energy minimum
• Existence of a Phase with Finite Localization Length in the Double Scaling Limit of N-Orbital Models