Regularity of the surface density of states. (English) Zbl 1005.82015
The authors find wide classes of continuous and discrete Anderson-type random Schrödinger operators for which the integrated surface density of states (a priori distribution) is actually a measurable locally integrable function. The proof is based on the \(L^p\)-bound on the spectral shift function obtained by J. M. Combes, P. D. Hislop and S. Nakamura [Commun. Math. Phys. 218, 113-130 (2001; Zbl 1042.82024)]. A new proof of the Hölder continuity of the integrated density of bulk states is also given.
Reviewer: Anatoly N.Kochubei (Kyïv)
MSC:
| 82B44 | Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics |
| 47B80 | Random linear operators |
| 60K40 | Other physical applications of random processes |
Keywords:
random Schrödinger operator; surface states; Anderson model; density of states; spectral shift functionCitations:
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