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- W2806862744 abstract "The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schrodinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {bf 173} (2001) 136-152]." @default.
- W2806862744 created "2018-06-13" @default.
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- W2806862744 date "2000-10-10" @default.
- W2806862744 modified "2023-09-23" @default.
- W2806862744 title "The integrated density of states and its absolute continuity for magnetic Schrodinger operators with unbounded random potentials" @default.
- W2806862744 hasPublicationYear "2000" @default.
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