Lifschitz tail in a magnetic field: The nonclassical regime

Probability Theory and Related Fields

Volumn 112, Issue 3, 1998, Pages 321-371

  Erdos, László ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032346360     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050193     Document Type: Article

References (27)

1. Aharonov, Y., Böhm, D.: Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485-491 (1959)
2. Aharonov, Y., Casher, A.: Ground state of spin-1/2 charged particle in a two-dimensional magnetic field. Phys. Rev. A19, 2461-2462 (1979)
3. Albeverio, S., Gesztesy, F., Hoegh-Krohn, R., Holden, H.: Solvable Models in Quantum Mechanics. Springer-Verlag (1988)
4. Brézin, E., Gross, D.J., Itzykson, C.: Density of states in the presence of a strong magnetic field and random impurities. Nucl. Phys. B 235, 24-44 (1984)
5. Broderix, K., Hundertmark, D., Kirsch, W., Leschke, H.: The fate of Lifshits tails in magnetic fields. J. Stat. Phys. 80, 1-22 (1995)
6. Broderix, K., Hundertmark, D., Leschke, H.: Self-averaging, decomposition and asymptotic properties of the density of states for random Schrödinger operators with constant magnetic field. In: Path Integrals from meV to MeV: Tutzing '92 World Sci. Publishing, River Edge, NJ, pp. 98-107 (1993)
7. Broderix, K., Hundertmark, D., Leschke, H.: Continuity properties of Schrödinger semigroups with magnetic fields. Preprint.
8. Cycon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger Operators with Application to Quantum Mechanics and Global Geometry. Springer-Verlag (1987)
9. Donsker, M.D., Varadhan, S.R.S.: Asymptotics for the Wiener sausage. Commun. Pure Appl. Math. 28, 525-566 (1975), Erratum: 28, 677 (1975)
10. Dorlas, T.C., Macris, N., Pulé, J.V.: The nature of the spectrum for a Landau Hamiltonian with delta impurities. J. Stat. Phys. 87, No. 3-4, 847-875 (1997)
11. Erdos, L.: Gaussian decay of the magnetic eigenfunctions. Geom. Funct. Anal. (GAFA) 6 No. 2, 231-248 (1996)
12. Erdos, L.: Rayleigh type isoperimetric inequality with a homogeneous magnetic field. Calc. Var. and PDE. 4, 283-292 (1996)
13. Erdos, L.: Dia- and paramagnetism for nonhomogeneous magnetic fields. Journal of Math. Phys. 38(3), 1289-1317 (1997)
14. Erdos, L., Solovej, J.P.: Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields. II. Leading order asymptotic estimates. Commun. Math. Phys. 188, 599-656 (1997)
15. Kirsch, W., Martinelli, F.: On the density of states of Schrödinger operators with a random potential. J. Phys. A 15, 2139-2156 (1982)
16. Klein, A., Perez, J.F.: On the density of states for random potentials in the presence of a uniform magnetic field. Nucl. Phys. B 251, 199-211 (1985)
17. Leinfelder, H.,: Gauge invariance of Schrödinger operators and related spectral properties. J. Op. Theor. 9, 163-179 (1983)
18. Macris, N., Pulé, J.V.: Density of states of random Schrödinger operators with a uniform magnetic field. Lett. Math. Phys. 24, 307-321 (1992)
19. Matsumoto, H.: On the integrated density of states for the Schrödinger operators with certain random electromagnetic potentials. J. Math. Soc. Japan 45, 197-214 (1993)
20. Pastur, L., Figotin, A.: Spectra of Random and Almost-periodic Operators. Berlin-Heidelberg-New York: Springer 1992.
21. Perez, J.F., Coutinho, F.A.B.: Schrödinger equation in two dimensions for a zero-range potential and a uniform magnetic field: An exactly solvable model. Am. J. Phys. 59, No. 1, 52-54 (1991)
22. Simon, B.: Semiclassical analysis of low lying eigenvalues. II. Tunneling. Ann. Math. 120, 89-118 (1984)
23. Simon, B.: Functional Integration and Quantum Physics. Academic Press N.Y. (1979)
24. Sznitman, A.S.: Lifschitz tail and Wiener sausage, I. J. Func. Anal. 94, 223-246 (1990)
25. Sznitman, A.S.: Brownian survival among Gibbsian traps. Ann. Probab. 21 No. 1, 490-508 (1993)
26. Sznitman, A.S.: Brownian asymptotics in a Poissonian environment. Prob. Th. Rel. Fields 95, 155-174 (1993)
27. Ueki, N.: On spectra of random Schrödinger operators with magnetic fields. Osaka J. Math. 31, 177-187 (1994)