Abstract
We obtain a bound on the expectation of the spectral shift function (SSF) for alloy-type random Schrodinger operators on R-d in the region of localisation, corresponding to a change from Dirichlet to Neumann boundary conditions along the boundary of a finite volume. The bound scales with the area of the surface where the boundary conditions are changed. As an application of our bound on the SSF, we prove a reverse Wegner inequality for finite-volume Schrodinger operators in the region of localisation with a constant locally uniform in the energy. The application requires that the single-site distribution of the independent and identically distributed random variables has a Lebesgue density that is also bounded away from zero. The reverse Wegner inequality implies a strictly positive, locally uniform lower bound on the density of states for these continuum random Schrodinger operators.
Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics |
Subjects: | 500 Science > 510 Mathematics |
ISSN: | 1073-7928 |
Language: | English |
Item ID: | 66379 |
Date Deposited: | 19. Jul 2019, 12:19 |
Last Modified: | 13. Aug 2024, 13:28 |