Spectra of Anderson type models with decaying randomness

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Volumn 111, Issue 2, 2001, Pages 179-201

  Krishna, M ^a,b   Sinha, K B ^a,b,c  

^a INSTITUTE OF MATHEMATICAL SCIENCES   (India)

^b INDIAN STATISTICAL INSTITUTE   (India)

^c INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Absolutely continuous spectrum; Anderson model; Decaying randomness; Mobility edge

Indexed keywords

EID: 0035328312     PISSN: 02534142     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02829590     Document Type: Article

References (21)

1. Aizenman M, Localization at weak disorder: Some elementary bounds, Rev. Math. Phys. 6 (1994) 1163-1182
2. Aizenman M and Graf S, Localization bounds for electron gas, preprint mp_arc 97-540 (1997)
3. Aizenman M and Molchanov S, Localization at large disorder and at extreme energies: an elementary derivation, Commun. Math. Phys. 157 (1993) 245-278
4. Boutet de Monvel A and Sahbani J, On the spectral properties of discrete Schrödinger operators, C. R. Acad. Sci. Paris, Series I 326 (1998) 1145-1150
5. Beutet de Monvel A and Sahbani J, On the spectral properties of discrete Schrödinger operators: multidimensional case, to appear in Rev. Math. Phys.
6. Carmona R and Lacroix J, Spectral theory of random Schrödinger operators (Boston: Birkhäuser Verlag) (1990)
7. Cycon H, Froese R, Kirsch W and Simon B, Topics in the Theory of Schrödinger operators (New York: Springer-Verlag, Berlin, Heidelberg) (1987)
8. Figotin A and Pastur L, Spectral properties of disordered systems in the one body approximation (Berlin, Heidelberg, New York: Springer-Verlag) (1991)
9. Kirsch W, Krishna M and Obermeit J. Anderson model with decaying randomness-mobility edge. Math. Zeit. (2000) DOI 10.1007/s002090000136
10. Krishna M, Anderson model with decaying randomness - Extended states, Proc. Indian. Acad. Sci. (Math. Sci.) 100 (1990) 220-240
11. Krishna M, Absolutely continuous spectrum for sparse potentials, Proc. Indian. Acad. Sci. (Math. Sci.), 103(3) (1993) 333-339
12. Krishna M and Obermeit J, Localization and mobility edge for sparsely random potentials, preprint xxx.lanl.gov/math-ph/9805015
13. Jaksic V and Last Y, Corrugated surfaces and a.c. spectrum (to appear in Rev. Math. Phys)
14. Jaksic V and Last Y, Spectral properties of Anderson type operators, Invent. Math. 141 (2000) 561-577
15. Jaksic V and Molchanov S, On the surface spectrum in dimension two, Helvetica Phys. Acta 71 (1999) 169-183
16. Jaksic V and Molchanov S, Localization of surface spectra, Commun. Math. Phys. 208 (1999) 153-172
17. Reed M and Simon B, Methods of modern mathematical physics: Functional analysis (New York: Academic Press) (1975)
18. Simon B, Spectral analysis of rank one perturbations and applications in CRM Lecture Notes (eds) J Feldman, R Froese, and L Rosen, Am. Math. Soc. 8 (1995) 109-149
19. Simon B and Wolff T, Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Comm. Pure Appl. Math. 39 (1986) 75-90
20. Stein E, Harmonic analysis - real variable methods, orthogonality and oscillatory integrals (New Jersey: Princeton University Press, Princeton) (1993)
21. Weidman J, Linear operators in Hilbert spaces, GTM-68 (Berlin: Springer-Verlag) (1987)