메뉴 건너뛰기




Volumn 221, Issue 2, 2001, Pages 229-254

The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035536778     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100467     Document Type: Article
Times cited : (35)

References (69)
  • 2
    • 85032069152 scopus 로고
    • Electronic properties of two-dimensional systems
    • 2. Ando, T., Fowler, A.B., Stern, F.: Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437-672 (1982)
    • (1982) Rev. Mod. Phys. , vol.54 , pp. 437-672
    • Ando, T.1    Fowler, A.B.2    Stern, F.3
  • 3
    • 84972547058 scopus 로고
    • Schrödinger operators with magnetic fields. I. General interactions
    • 3. Avron, J., Herbst, I., Simon, B.: Schrödinger operators with magnetic fields. I. General interactions. Duke Math. J. 45, 847-883 (1978)
    • (1978) Duke Math. J. , vol.45 , pp. 847-883
    • Avron, J.1    Herbst, I.2    Simon, B.3
  • 4
    • 0002271908 scopus 로고    scopus 로고
    • Localization near band edges for random Schrödinger operators
    • 4. Barbaroux, J.-M., Combes, J.M., Hislop, P.D.: Localization near band edges for random Schrödinger operators. Helv. Phys. Acta 70, 16-43 (1997)
    • (1997) Helv. Phys. Acta , vol.70 , pp. 16-43
    • Barbaroux, J.-M.1    Combes, J.M.2    Hislop, P.D.3
  • 5
    • 0007130625 scopus 로고    scopus 로고
    • Landau Hamiltonians with unbounded random potentials
    • 5. Barbaroux, J.-M., Combes, J.M., Hislop, P.D.: Landau Hamiltonians with unbounded random potentials. Lett. Math. Phys. 40, 335-369 (1997)
    • (1997) Lett. Math. Phys. , vol.40 , pp. 335-369
    • Barbaroux, J.-M.1    Combes, J.M.2    Hislop, P.D.3
  • 6
    • 0007082802 scopus 로고
    • Auflage, Berlin: de Gruyter, [in German] English translation to appear
    • 6. Bauer, H.: Maβ-und Integrationstheorie. 2. Auflage, Berlin: de Gruyter, 1992 [in German] English translation to appear
    • (1992) Maβ-und Integrationstheorie , vol.2
    • Bauer, H.1
  • 8
    • 0002693424 scopus 로고
    • Self-averaging, decomposition and asymptotic properties of the density of states for random Schrödinger operators with constant magnetic field
    • Grabert, H., Inomata, A., Schulman, L.S., Weiss, U. (eds.), Singapore: World Scientific
    • 8. 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. Grabert, H., Inomata, A., Schulman, L.S., Weiss, U. (eds.), Singapore: World Scientific, 1993, pp. 98-107
    • (1993) Path Integrals from meV to MeV: Tutzing '92 , pp. 98-107
    • Broderix, K.1    Hundertmark, D.2    Leschke, H.3
  • 9
    • 0034395580 scopus 로고    scopus 로고
    • Continuity properties of Schrödinger semigroups with magnetic fields
    • 9. Broderix, K., Hundertmark, D., Leschke, H.: Continuity properties of Schrödinger semigroups with magnetic fields. Rev. Math. Phys. 12, 181-225 (2000)
    • (2000) Rev. Math. Phys. , vol.12 , pp. 181-225
    • Broderix, K.1    Hundertmark, D.2    Leschke, H.3
  • 11
    • 0001026869 scopus 로고
    • Localization for some continuous, random Hamiltonians in d-dimensions
    • 11. Combes, J.M., Hislop, P.D.: Localization for some continuous, random Hamiltonians in d-dimensions. J. Funct. Anal. 124, 149-180 (1994)
    • (1994) J. Funct. Anal. , vol.124 , pp. 149-180
    • Combes, J.M.1    Hislop, P.D.2
  • 12
    • 0000059896 scopus 로고    scopus 로고
    • Landau Hamiltonians with random potentials: Localization and the density of states
    • 12. Combes, J.M., Hislop, P.D.: Landau Hamiltonians with random potentials: Localization and the density of states. Commun. Math. Phys. 177, 603-629 (1996)
    • (1996) Commun. Math. Phys. , vol.177 , pp. 603-629
    • Combes, J.M.1    Hislop, P.D.2
  • 13
    • 21444432939 scopus 로고    scopus 로고
    • Spectral averaging, perturbation of singular spectra, and localization
    • 13. Combes, J.M., Hislop, P.D., Mourre, E.: Spectral averaging, perturbation of singular spectra, and localization. Trans. Am. Math. Soc. 348, 4883-4894 (1996)
    • (1996) Trans. Am. Math. Soc. , vol.348 , pp. 4883-4894
    • Combes, J.M.1    Hislop, P.D.2    Mourre, E.3
  • 14
    • 0002221209 scopus 로고
    • Classical bounds and limits for energy distributions of Hamilton operators in electromagnetic fields
    • 14. Combes, J.M., Schrader, R., Seiler, R.: Classical bounds and limits for energy distributions of Hamilton operators in electromagnetic fields. Ann. Phys. (N.Y.) 111, 1-18 (1978)
    • (1978) Ann. Phys. (N.Y.) , vol.111 , pp. 1-18
    • Combes, J.M.1    Schrader, R.2    Seiler, R.3
  • 15
    • 0001449373 scopus 로고
    • Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices
    • 15. Craig, W., Simon, B.: Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices. Commun. Math. Phys. 90, 207-218 (1983)
    • (1983) Commun. Math. Phys. , vol.90 , pp. 207-218
    • Craig, W.1    Simon, B.2
  • 17
  • 18
    • 0000010934 scopus 로고
    • Remark on the continuity of the density of states of ergodic finite difference operators
    • 18. Delyon, F., Souillard, B.: Remark on the continuity of the density of states of ergodic finite difference operators. Commun. Math. Phys. 94, 289-291 (1984)
    • (1984) Commun. Math. Phys. , vol.94 , pp. 289-291
    • Delyon, F.1    Souillard, B.2
  • 19
    • 0035534688 scopus 로고    scopus 로고
    • The uniqueness of the integrated density of states for the Schrödinger operators with magnetic fields
    • 19. Doi, S., Iwatsuka, A., Mine, T.: The uniqueness of the integrated density of states for the Schrödinger operators with magnetic fields. Math. Z. 237, 335-371 (2001)
    • (2001) Math. Z. , vol.237 , pp. 335-371
    • Doi, S.1    Iwatsuka, A.2    Mine, T.3
  • 20
    • 0033241786 scopus 로고    scopus 로고
    • Characterization of the spectrum of the Landau Hamiltonian with delta impurities
    • 20. Dorlas, T.C., Macris, N., Pulé, J.V.: Characterization of the spectrum of the Landau Hamiltonian with delta impurities. Commun. Math. Phys. 204, 367-396 (1999)
    • (1999) Commun. Math. Phys. , vol.204 , pp. 367-396
    • Dorlas, T.C.1    Macris, N.2    Pulé, J.V.3
  • 21
    • 38249041049 scopus 로고
    • The effect of boundary conditions on the density of states for random Schrödinger operators
    • 21. Droese, J., Kirsch, W.: The effect of boundary conditions on the density of states for random Schrödinger operators. Stochastic Processes Appl. 23, 169-175 (1986)
    • (1986) Stochastic Processes Appl. , vol.23 , pp. 169-175
    • Droese, J.1    Kirsch, W.2
  • 22
    • 0001783943 scopus 로고
    • Regularité des trajectoires des fonctions aléatoires gaussiennes
    • Ecole d'Eté de Probabilités de Saint-Flour IV - 1974. Hennequin, P.-L. (ed.), Berlin: Springer, [in French]
    • 22. Fernique, X.M.: Regularité des trajectoires des fonctions aléatoires Gaussiennes. In: Ecole d'Eté de Probabilités de Saint-Flour IV - 1974. Hennequin, P.-L. (ed.), Lecture Notes in Mathematics 480, Berlin: Springer, 1975, pp. 1-96 [in French]
    • (1975) Lecture Notes in Mathematics , vol.480 , pp. 1-96
    • Fernique, X.M.1
  • 23
    • 0039054598 scopus 로고    scopus 로고
    • Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials
    • 23. Fischer, W., Hupfer, T., Leschke, H., Müller, P.: Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials. Commun. Math. Phys. 190, 133-141 (1997)
    • (1997) Commun. Math. Phys. , vol.190 , pp. 133-141
    • Fischer, W.1    Hupfer, T.2    Leschke, H.3    Müller, P.4
  • 24
    • 0034549703 scopus 로고    scopus 로고
    • Spectral localization by Gaussian random potentials in multidimensional continuous space
    • 24. Fischer, W., Leschke, H., Müller, P.: Spectral localization by Gaussian random potentials in multidimensional continuous space. J. Stat. Phys. 101, 935-985 (2000)
    • (2000) J. Stat. Phys. , vol.101 , pp. 935-985
    • Fischer, W.1    Leschke, H.2    Müller, P.3
  • 25
    • 33646622306 scopus 로고
    • Bemerkung zur Quantelung des harmonischen Oszillators im Magnetfeld
    • in German
    • 25. Fock, V.: Bemerkung zur Quantelung des harmonischen Oszillators im Magnetfeld. Z. Physik 47, 446-448 (1928) [in German]
    • (1928) Z. Physik , vol.47 , pp. 446-448
    • Fock, V.1
  • 28
    • 84972582297 scopus 로고
    • Domination of semigroups and generalization of Kato's inequality
    • 28. Hess, H., Schrader, R., Uhlenbrock, D.A.: Domination of semigroups and generalization of Kato's inequality. Duke Math. J. 44, 893-904 (1977)
    • (1977) Duke Math. J. , vol.44 , pp. 893-904
    • Hess, H.1    Schrader, R.2    Uhlenbrock, D.A.3
  • 31
    • 51249191546 scopus 로고
    • Schrödinger operators with singular potentials
    • 31. Kalo, T.: Schrödinger operators with singular potentials. Israel J. Math. 13, 135-148 (1972)
    • (1972) Israel J. Math. , vol.13 , pp. 135-148
    • Kalo, T.1
  • 32
    • 0000046855 scopus 로고
    • Remarks on Schrödinger operators with vector potentials
    • 32. Kato, T.: Remarks on Schrödinger operators with vector potentials. Integral Equations Oper. Theory 1, 103-113 (1978)
    • (1978) Integral Equations Oper. Theory , vol.1 , pp. 103-113
    • Kato, T.1
  • 33
    • 84972537190 scopus 로고
    • Trotter's product formula for nonlinear semigroups generated by the subdifferentials of convex functionals
    • 33. Kato, T., Masuda, K.: Trotter's product formula for nonlinear semigroups generated by the subdifferentials of convex functionals. J. Math. Soc. Japan 30, 169-178 (1978)
    • (1978) J. Math. Soc. Japan , vol.30 , pp. 169-178
    • Kato, T.1    Masuda, K.2
  • 34
    • 0000818766 scopus 로고
    • Random Schrödinger operators: A course
    • Schrödinger operators. Holden, H., Jensen, A. (eds.), Berlin: Springer
    • 34. Kirsch, W.: Random Schrödinger operators: A course. In: Schrödinger operators. Holden, H., Jensen, A. (eds.), Lecture Notes in Physics 345, Berlin: Springer, 1989, pp. 264-370
    • (1989) Lecture Notes in Physics , vol.345 , pp. 264-370
    • Kirsch, W.1
  • 35
    • 0000112074 scopus 로고
    • On the ergodic properties of the spectrum of general random operators
    • 35. Kirsch, W., Martinelli, F.: On the ergodic properties of the spectrum of general random operators. J. Reine Angew. Math. 334, 141-156 (1982)
    • (1982) J. Reine Angew. Math. , vol.334 , pp. 141-156
    • Kirsch, W.1    Martinelli, F.2
  • 36
    • 0000059648 scopus 로고
    • On the density of states of Schrödinger operators with a random potential
    • 36. Kirsch, W., Martinelli, F.: On the density of states of Schrödinger operators with a random potential. J. Phys. A 15, 2139-2156 (1982)
    • (1982) J. Phys. A , vol.15 , pp. 2139-2156
    • Kirsch, W.1    Martinelli, F.2
  • 37
    • 84927873999 scopus 로고
    • Two-dimensional electron density of states in a transverse magnetic field
    • 37. Kukushkin, I.V., Meshkov, S. V., Timofeev, V.B.: Two-dimensional electron density of states in a transverse magnetic field. Sov. Phys. Usp. 31, 511-534 (1988) [Russian original: Usp. Fiz. Nauk 155, 219-264 (1988)]
    • (1988) Sov. Phys. Usp. , vol.31 , pp. 511-534
    • Kukushkin, I.V.1    Meshkov, S.V.2    Timofeev, V.B.3
  • 38
    • 84927873999 scopus 로고
    • 37. Kukushkin, I.V., Meshkov, S. V., Timofeev, V.B.: Two-dimensional electron density of states in a transverse magnetic field. Sov. Phys. Usp. 31, 511-534 (1988) [Russian original: Usp. Fiz. Nauk 155, 219-264 (1988)]
    • (1988) Usp. Fiz. Nauk , vol.155 , pp. 219-264
  • 39
    • 34250934540 scopus 로고
    • Diamagnetismus der Metalle
    • in German
    • 38. Landau, L.: Diamagnetismus der Metalle. Z. Physik 64, 629-637 (1930) [in German]
    • (1930) Z. Physik , vol.64 , pp. 629-637
    • Landau, L.1
  • 40
    • 0004148844 scopus 로고    scopus 로고
    • Providence, Rhode Island: Am. Math. Soc.
    • 39. Lieb, E.H., Loss, M.: Analysis. Providence, Rhode Island: Am. Math. Soc., 1997
    • (1997) Analysis
    • Lieb, E.H.1    Loss, M.2
  • 43
    • 0031574595 scopus 로고    scopus 로고
    • Dominated semigroups with singular complex potentials
    • 42. Liskevitch, V., Manavi, A.: Dominated semigroups with singular complex potentials. J. Funct. Anal. 151, 281-305 (1997)
    • (1997) J. Funct. Anal. , vol.151 , pp. 281-305
    • Liskevitch, V.1    Manavi, A.2
  • 44
    • 84972572897 scopus 로고
    • On the integrated density of states for the Schrödinger operators with certain random electromagnetic potentials
    • 43. 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)
    • (1993) J. Math. Soc. Japan , vol.45 , pp. 197-214
    • Matsumoto, H.1
  • 45
    • 0011006814 scopus 로고
    • On the spectral theory of the Schrödinger operator with electromagnetic potential
    • Demuth, M., Schrohe, E., Schulze, B.-W.(eds.), Berlin: Akademie
    • 44. Mohamed, A., Raikov, G.D.: On the spectral theory of the Schrödinger operator with electromagnetic potential. In: Pseudo-differential calculus and mathematical physics. Demuth, M., Schrohe, E., Schulze, B.-W.(eds.), Berlin: Akademie, 1994, pp. 298-390
    • (1994) Pseudo-differential Calculus and Mathematical Physics , pp. 298-390
    • Mohamed, A.1    Raikov, G.D.2
  • 46
    • 0003035749 scopus 로고    scopus 로고
    • A remark on the Dirichlet-Neumann decoupling and the integrated density of states
    • 45. Nakamura, S.: A remark on the Dirichlet-Neumann decoupling and the integrated density of states. J. Fund. Anal. 179, 136-152 (2001)
    • (2001) J. Fund. Anal. , vol.179 , pp. 136-152
    • Nakamura, S.1
  • 47
    • 0000188166 scopus 로고
    • On the spectral distribution of the Schrödinger operator with random potential
    • 46. Nakao, S.: On the spectral distribution of the Schrödinger operator with random potential. Japan. J. Math. 3, 111-139 (1977)
    • (1977) Japan. J. Math. , vol.3 , pp. 111-139
    • Nakao, S.1
  • 48
    • 0007137847 scopus 로고
    • On the Schrödinger equation with a random potential
    • 47. Pastur, L.: On the Schrödinger equation with a random potential. Theor. Math. Phys. 6, 299-306 (1971) [Russian original: Teor. Mat. Fiz. 6, 415-424 (1971)]
    • (1971) Theor. Math. Phys. , vol.6 , pp. 299-306
    • Pastur, L.1
  • 49
    • 0007137847 scopus 로고
    • 47. Pastur, L.: On the Schrödinger equation with a random potential. Theor. Math. Phys. 6, 299-306 (1971) [Russian original: Teor. Mat. Fiz. 6, 415-424 (1971)]
    • (1971) Teor. Mat. Fiz. , vol.6 , pp. 415-424
  • 50
    • 34250250635 scopus 로고
    • Spectral properties of disordered systems in the one-body approximation
    • 48. Pastur, L.: Spectral properties of disordered systems in the one-body approximation. Commun. Math. Phys. 75, 179-196 (1980)
    • (1980) Commun. Math. Phys. , vol.75 , pp. 179-196
    • Pastur, L.1
  • 52
    • 0000867030 scopus 로고
    • On decoupling of finite singularities in the scattering theory for the Schrödinger operator with a magnetic field
    • 50. Perelmuter, M.A., Semenov, Yu.A.: On decoupling of finite singularities in the scattering theory for the Schrödinger operator with a magnetic field. J. Math. Phys. 22, 521-533 (1981)
    • (1981) J. Math. Phys. , vol.22 , pp. 521-533
    • Perelmuter, M.A.1    Semenov, Yu.A.2
  • 57
    • 0000488253 scopus 로고
    • Universal diamagnetism of spinless Bose systems
    • 55. Simon, B.: Universal diamagnetism of spinless Bose systems. Phys. Rev. Lett. 36, 1083-1084 (1976)
    • (1976) Phys. Rev. Lett. , vol.36 , pp. 1083-1084
    • Simon, B.1
  • 58
    • 0001518364 scopus 로고
    • An abstract Kato's inequality for generators of positivity preserving semigroups
    • 56. Simon, B.: An abstract Kato's inequality for generators of positivity preserving semigroups. Ind. Math. J. 26, 1067-1073 (1977)
    • (1977) Ind. Math. J. , vol.26 , pp. 1067-1073
    • Simon, B.1
  • 59
    • 0002596898 scopus 로고
    • Maximal and minimal Schrödinger forms
    • 57. Simon, B.: Maximal and minimal Schrödinger forms. J. Operator Theory 1, 37-47 (1979)
    • (1979) J. Operator Theory , vol.1 , pp. 37-47
    • Simon, B.1
  • 61
    • 0002093591 scopus 로고
    • Kato's inequality and the comparison of semigroups
    • 59. Simon, B.: Kato's inequality and the comparison of semigroups. J. Funct. Anal. 32, 97-101 (1979)
    • (1979) J. Funct. Anal. , vol.32 , pp. 97-101
    • Simon, B.1
  • 62
    • 0003273202 scopus 로고    scopus 로고
    • Schrödinger operators in the twenty-first century
    • Fokas, A., Grigoryan, A., Kibble, T., Zegarlinski, B. (eds.), London: Imperial College Press
    • 60. Simon, B.: Schrödinger operators in the twenty-first century. In: Mathematical Physics 2000. Fokas, A., Grigoryan, A., Kibble, T., Zegarlinski, B. (eds.), London: Imperial College Press, 2000, pp. 283-288
    • (2000) Mathematical Physics 2000 , pp. 283-288
    • Simon, B.1
  • 64
    • 84972571649 scopus 로고
    • On spectra of random Schrödinger operators with magnetic fields
    • 62. Ueki, N.: On spectra of random Schrödinger operators with magnetic fields. Osaka J. Math. 31, 177-187 (1994)
    • (1994) Osaka J. Math. , vol.31 , pp. 177-187
    • Ueki, N.1
  • 66
    • 0031142034 scopus 로고    scopus 로고
    • Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential
    • 64. Wang, W.-M.: Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential. J. Funct. Anal. 146, 1-26 (1997)
    • (1997) J. Funct. Anal. , vol.146 , pp. 1-26
    • Wang, W.-M.1
  • 67
    • 0002037112 scopus 로고
    • Bounds on the density of states in disordered systems
    • 65. Wegner, F.: Bounds on the density of states in disordered systems. Z. Phys. B 44, 9-15 (1981)
    • (1981) Z. Phys. B , vol.44 , pp. 9-15
    • Wegner, F.1
  • 68
    • 0001117305 scopus 로고
    • Das asymptotische verteilungsgesetz der eigenwerte linearer partieller differentialgleichungen (mit einer anwendung auf die theorie der hohlraumstrahlung)
    • in German
    • 66. Weyl, H.: Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung). Math. Ann. 71, 441-479 (1912) [in German]
    • (1912) Math. Ann. , vol.71 , pp. 441-479
    • Weyl, H.1
  • 69
    • 36149008019 scopus 로고
    • Magnetic translation group
    • 67. Zak, J.: Magnetic translation group. Phys. Rev. 134, A1602-A1606 (1964)
    • (1964) Phys. Rev. , vol.134
    • Zak, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.