THE DENSITY OF STATES AND THE SPECTRAL SHIFT DENSITY OF RANDOM SCHRÖDINGER OPERATORS

DOI10.1142/S0129055X00000320zbMath0961.47022arXivmath-ph/0011033OpenAlexW3106274331MaRDI QIDQ4519858

Vadim Kostrykin, Robert Schrader

Publication date: 4 December 2000

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0011033

zbMATH Keywords

random Schrödinger operatorsscattering theoryeigenvalue counting functioninteraction theorybulk limit of the spectral shift function per unit interaction volumeintegrated densities of states

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Perturbation theory of linear operators (47A55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Random linear operators (47B80) Quantum scattering theory (81U99) Scattering theory of linear operators (47A40)

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The band-edge behavior of the density of surfacic states ⋮ Weak convergence of spectral shift functions for one‐dimensional Schrödinger operators ⋮ The spectral shift function for compactly supported perturbations of Schrödinger operators on large bounded domains ⋮ Wegner estimates for some random operators with Anderson-type surface potentials ⋮ The generalized star product and the factorization of scattering matrices on graphs ⋮ EXISTENCE AND UNIQUENESS OF THE INTEGRATED DENSITY OF STATES FOR SCHRÖDINGER OPERATORS WITH MAGNETIC FIELDS AND UNBOUNDED RANDOM POTENTIALS ⋮ Regularity of the surface density of states ⋮ An optimal \(L^p\)-bound on the Krein spectral shift function. ⋮ Concavity of eigenvalue sums and the spectral shift function ⋮ The Wegner estimate and the integrated density of states for some random operators ⋮ Wegner estimate for sparse and other generalized alloy type potentials ⋮ The integrated density of states for some random operators with nonsign definite potentials ⋮ Anderson localization and Lifshits tails for random surface potentials

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