Supersymmetry and density of states of the magnetic Schrödinger operator with a random potential revisited

Communications in Partial Differential Equations

Volumn 25, Issue 3-4, 2000, Pages 601-679

  Wang, Wei Min ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013289253     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605300008821526     Document Type: Article

References (26)

1. A. Abdesselam, V. Rivasseau, Trees, forests and jungles: a botanical garden, Constructive Physics, Lecture Notes in Physics, 446, 1994.
2. J. Bellissard, A. van Elst, and H. Schulz-Baldes, The non-commutative geometry of the quantum Hall effect, J. Math. Phys. (1994).
3. F. A. Berezin, The Method of Second Quantization, Academic Press, New York, 1966.
4. M. Berger, B. Gostiaux, Géométrie Différentielle; Variétés, Courbes et Surfaces, Presses Universitaires de France, 1987.
5. N. Berline, E. Getzler and M. Vergne, Heat kernels and Dirac operators, Springer-Verlag, 1992.
6. N. Bourbaki, Eléments de mathématiques. Topologie générale. II. Structures uniformes, Masson.
7. N. Bourbaki, Eléments de mathématiques. Topologie générale. IX. Application des nombres réels, Masson.
8. A. Bovier, M. Campanino, A. Klein, and F. Perez, Smoothness of the density of states in the Anderson model at high disorder, Commun. Math. Phys. 114 (1988), 439-461.
9. D. Brydges, T. Kennedy, Mayer expansions and the Hamilton-Jacobi equation, J. Stat. Phys. 48 (1987).
10. K. Broderix, D. Hundertmark, W. Kirsch, H. Leschke, The fate of Lifshits tails in magnetic field, J. of Stat. Phys. 80 (1995).
11. J. M. Combes, P. D. Hislop, Landau Hamiltonians with random potentials: localization and density of states, Commun. Math. Phys. 177 (1996).
12. A. Grigis, J. Sjöstrand, Microlocal analysis for differential operators, Cambridge University Press, 1994.
13. B. Helffer, J. Sjöstrand, Équation de Schrödinger avec champ magnétique et équation de Harper, Lecture Notes in Physics 345, 1989.
14. A. Klein, The supersymmetric replica trick and smoothness of the density of states for the random Schrödinger operators, Proceedings of Symposium in Pure Mathematics 51 (1990).
15. A. Klein, J-F. Perez, On the density of states for random potentials in the presence of a uniform magnetic field, Nucl. Phys. B 251 (1985).
16. A. Klein, A. Spies, Smoothness of the density of states in the Anderson model on a one dimensional strip, Annals of Physics 183 (1988), 352-398.
17. F. Klopp, An asymptotic expansion for the density of states of a random Schrödinger operator with Bernoulli disorder, Random Oper. Stochastic Equations 3 3 (1995), 315-331.
18. F. Klopp, A low concentration asymptotic expansion for the density of states of a random Schrödinger operator with Poisson disorder, J. Funct. Anal. 145 (1997), 267-295.
19. N. Macris, J. V. Pule, Density of states of random Schrödinger operators with a uniform magnetic field, Lett. Math. Phys. 24 (1992), 307-321.
20. V. Rivasseau, From Perturbative to Constructive Renormalization, Princeton University Press, 1992.
21. B. Simon, Schrödinger semigroups, Bull. Am. Math. Soc. 7 (1982), 447-526.
22. J. Sjöstrand, Microlocal analysis for the periodic magnetic Schrödinger equation and related questions, Lecture Notes in Math. 1495, 1989.
23. T. Voronov, Geometric Integration Theory on Supermanifolds, Mathematical Physics Review, USSR Academy of Sciences, Moscow, 1993.
24. W. M. Wang, Asymptotic expansion for the density of states of the magnetic Schrödinger operator with a random potential, Commun. Math. Phys. 172 (1995), 401-425.
25. W. M. Wang, Microlocalization, Percolation and Anderson localization for the magnetic Schrödinger operator with a random potential, J. of Func. Anal. 146 (1997), 1-26.
26. F. Wegner, Bounds on the density of states in disordered systems, Z. Phys. B44 (1981), 9-15.