메뉴 건너뛰기




Volumn 226, Issue 2, 2005, Pages 301-372

Linear response theory for magnetic Schrödinger operators in disordered media

Author keywords

Kubo formula; Kubo Streda formula; Magnetic Schr dinger operator

Indexed keywords


EID: 23844514826     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.02.002     Document Type: Article
Times cited : (66)

References (43)
  • 1
    • 1142298215 scopus 로고    scopus 로고
    • Moment analysis for localization in random Schrödinger operators
    • preprint, math-ph/0308023
    • M. Aizenman, A. Elgart, S. Naboko, J.H. Schenker, G. Stolz, Moment analysis for localization in random Schrödinger operators, 2003 preprint, math-ph/0308023.
    • (2003)
    • Aizenman, M.1    Elgart, A.2    Naboko, S.3    Schenker, J.H.4    Stolz, G.5
  • 2
    • 23844525435 scopus 로고    scopus 로고
    • Adiabatic charge transport, localization, and the Kubo formula for 2 D Hall conductance in a gapless state
    • in preparation
    • M. Aizenman, A. Elgart, J.H. Schenker, Adiabatic charge transport, localization, and the Kubo formula for 2 D Hall conductance in a gapless state, in preparation.
    • Aizenman, M.1    Elgart, A.2    Schenker, J.H.3
  • 3
    • 0032516668 scopus 로고    scopus 로고
    • Localization bounds for an electron gas
    • M. Aizenman G.M. Graf Localization bounds for an electron gas J. Phys. A: Math. Gen. 31 1998 6783-6806
    • (1998) J. Phys. A: Math. Gen. , vol.31 , pp. 6783-6806
    • Aizenman, M.1    Graf, G.M.2
  • 4
    • 21344496244 scopus 로고
    • Charge deficiency, charge transport and comparison of dimensions
    • J. Avron R. Seiler B. Simon Charge deficiency, charge transport and comparison of dimensions Comm. Math. Phys. 159 1994 399-422
    • (1994) Comm. Math. Phys. , vol.159 , pp. 399-422
    • Avron, J.1    Seiler, R.2    Simon, B.3
  • 5
    • 0009907303 scopus 로고
    • Ordinary quantum Hall effect and noncommutative cohomology
    • (Bad Schandau, 1986), Teubner-Texte Phys. Teubner
    • J. Bellissard, Ordinary quantum Hall effect and noncommutative cohomology, in: Localization in disordered systems (Bad Schandau, 1986), Teubner-Texte Phys., vol. 16, Teubner, 1988, pp. 61-74.
    • (1988) Localization in Disordered Systems , vol.16 , pp. 61-74
    • Bellissard, J.1
  • 6
    • 21844487920 scopus 로고
    • The non commutative geometry of the quantum Hall effect
    • J. Bellissard A. van Elst H. Schulz-Baldes The non commutative geometry of the quantum Hall effect J. Math. Phys. 35 1994 5373-5451
    • (1994) J. Math. Phys. , vol.35 , pp. 5373-5451
    • Bellissard, J.1    van Elst, A.2    Schulz-Baldes, H.3
  • 7
    • 0008732773 scopus 로고
    • On the point spectrum of Dirac operators
    • A. Berthier V. Georgescu On the point spectrum of Dirac operators J. Funct. Anal. 71 1987 309-338
    • (1987) J. Funct. Anal. , vol.71 , pp. 309-338
    • Berthier, A.1    Georgescu, V.2
  • 8
    • 4344621090 scopus 로고    scopus 로고
    • Sub-exponential decay of operator kernels for functions of generalized Schrödinger operators
    • J.M. Bouclet F. Germinet A. Klein Sub-exponential decay of operator kernels for functions of generalized Schrödinger operators Proc. Amer. Math. Soc. 132 2004 2703-2712
    • (2004) Proc. Amer. Math. Soc. , vol.132 , pp. 2703-2712
    • Bouclet, J.M.1    Germinet, F.2    Klein, A.3
  • 10
    • 0000059896 scopus 로고    scopus 로고
    • Landau Hamiltonians with random potentials: Localization and the density of states
    • J.M. Combes P.D. Hislop Landau Hamiltonians with random potentials localization and the density of states Comm. Math. Phys. 177 1996 603-629
    • (1996) Comm. Math. Phys. , vol.177 , pp. 603-629
    • Combes, J.M.1    Hislop, P.D.2
  • 11
    • 33847654434 scopus 로고
    • Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators
    • J.M. Combes L. Thomas Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators Comm. Math. Phys. 34 1973 251-270
    • (1973) Comm. Math. Phys. , vol.34 , pp. 251-270
    • Combes, J.M.1    Thomas, L.2
  • 12
    • 23844484236 scopus 로고    scopus 로고
    • A rigorous proof for the Landauer-Büttiker formula
    • preprint on mp_arc 04-71
    • H.D. Cornean, A. Jensen, V. Moldoveanu, A rigorous proof for the Landauer-Büttiker formula, preprint on mp_arc 04-71.
    • Cornean, H.D.1    Jensen, A.2    Moldoveanu, V.3
  • 14
    • 0013532445 scopus 로고
    • Kernel estimates for functions of second order elliptic operators
    • E.B. Davies Kernel estimates for functions of second order elliptic operators Quart. J. Math. Oxford (2) 39 1988 37-46
    • (1988) Quart. J. Math. Oxford , vol.39 , Issue.2 , pp. 37-46
    • Davies, E.B.1
  • 15
    • 2442520303 scopus 로고    scopus 로고
    • Adiabatic charge transport and the Kubo formula for Landau type Hamiltonians
    • A. Elgart B. Schlein Adiabatic charge transport and the Kubo formula for Landau type Hamiltonians Comm. Pure Appl. Math. 57 2004 590-615
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 590-615
    • Elgart, A.1    Schlein, B.2
  • 17
    • 0035538238 scopus 로고    scopus 로고
    • Bootstrap multiscale analysis and localization in random media
    • F. Germinet A. Klein Bootstrap multiscale analysis and localization in random media Commun. Math. Phys. 222 2001 415-448
    • (2001) Commun. Math. Phys. , vol.222 , pp. 415-448
    • Germinet, F.1    Klein, A.2
  • 18
    • 0037374309 scopus 로고    scopus 로고
    • Operator kernel estimates for functions of generalized Schrödinger operators
    • F. Germinet A. Klein Operator kernel estimates for functions of generalized Schrödinger operators Proc. Amer. Math. Soc. 131 2003 911-920
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 911-920
    • Germinet, F.1    Klein, A.2
  • 19
    • 1142264344 scopus 로고    scopus 로고
    • Explicit finite volume criteria for localization in continuous random media and applications
    • F. Germinet A. Klein Explicit finite volume criteria for localization in continuous random media and applications Geom. Funct. Anal. 13 2003 1201-1238
    • (2003) Geom. Funct. Anal. , vol.13 , pp. 1201-1238
    • Germinet, F.1    Klein, A.2
  • 20
    • 4644231405 scopus 로고    scopus 로고
    • A characterization of the Anderson metal-insulator transport transition
    • F. Germinet A. Klein A characterization of the Anderson metal-insulator transport transition Duke Math. J. 124 2004 309-351
    • (2004) Duke Math. J. , vol.124 , pp. 309-351
    • Germinet, F.1    Klein, A.2
  • 21
    • 23844549932 scopus 로고    scopus 로고
    • New characterizations of the region of complete localization for random Schrödinger operators
    • Preprint
    • F. Germinet, A. Klein, New characterizations of the region of complete localization for random Schrödinger operators. Preprint.
    • Germinet, F.1    Klein, A.2
  • 22
    • 0000301201 scopus 로고
    • Equation de Schrödinger avec champ magnétique et équation de Harper
    • H. Holden A. Jensen (Eds.), Springer Berlin
    • B. Helffer J. Sjöstrand Equation de Schrödinger avec champ magnétique et équation de Harper in: H. Holden A. Jensen (Eds.), Schrödinger Operators, Lectures Notes in Physics vol. 345 1989 Springer Berlin 118-197
    • (1989) Schrödinger Operators, Lectures Notes in Physics , vol.345 , pp. 118-197
    • Helffer, B.1    Sjöstrand, J.2
  • 23
    • 0034376103 scopus 로고    scopus 로고
    • Time-dependent scattering theory for N-body quantum systems
    • W. Hunziker I.M. Sigal Time-dependent scattering theory for N-body quantum systems Rev. Math. Phys. 12 2000 1033-1084
    • (2000) Rev. Math. Phys. , vol.12 , pp. 1033-1084
    • Hunziker, W.1    Sigal, I.M.2
  • 25
    • 1842733448 scopus 로고    scopus 로고
    • Quantization of edge currents for continuous magnetic operators
    • J. Kellendonk H. Schulz-Baldes Quantization of edge currents for continuous magnetic operators J. Funct. Anal. 209 2004 388-413
    • (2004) J. Funct. Anal. , vol.209 , pp. 388-413
    • Kellendonk, J.1    Schulz-Baldes, H.2
  • 26
    • 0000052706 scopus 로고
    • The quantum Hall effect for electrons in a random potential
    • H. Kunz The quantum Hall effect for electrons in a random potential Comm. Math. Phys. 112 1987 121-145
    • (1987) Comm. Math. Phys. , vol.112 , pp. 121-145
    • Kunz, H.1
  • 27
    • 0001815299 scopus 로고
    • Schrödinger operators with singular magnetic potentials
    • H. Leinfelder C.G. Simader Schrödinger operators with singular magnetic potentials Math. Z. 176 1981 1-19
    • (1981) Math. Z. , vol.176 , pp. 1-19
    • Leinfelder, H.1    Simader, C.G.2
  • 28
    • 0000239791 scopus 로고
    • Low energy bands do not contribute to quantum Hall effect
    • S. Nakamura J. Bellissard Low energy bands do not contribute to quantum Hall effect Comm. Math. Phys. 131 1990 283-305
    • (1990) Comm. Math. Phys. , vol.131 , pp. 283-305
    • Nakamura, S.1    Bellissard, J.2
  • 29
    • 0036014362 scopus 로고    scopus 로고
    • Absence of transport in Anderson localization
    • F. Nakano Absence of transport in Anderson localization Rev. Math. Phys. 14 2002 375-407
    • (2002) Rev. Math. Phys. , vol.14 , pp. 375-407
    • Nakano, F.1
  • 30
    • 34250250635 scopus 로고
    • Spectral properties of disordered systems in the one-body approximation
    • L. Pastur Spectral properties of disordered systems in the one-body approximation Comm. Math. Phys. 75 1980 179-196
    • (1980) Comm. Math. Phys. , vol.75 , pp. 179-196
    • Pastur, L.1
  • 35
  • 36
    • 0032092299 scopus 로고    scopus 로고
    • A kinetic theory for quantum transport in aperiodic media
    • H. Schulz-Baldes J. Bellissard A kinetic theory for quantum transport in aperiodic media J. Statist. Phys. 91 1998 991-1026
    • (1998) J. Statist. Phys. , vol.91 , pp. 991-1026
    • Schulz-Baldes, H.1    Bellissard, J.2
  • 37
    • 0002596898 scopus 로고
    • Maximal and minimal Schrödinger forms
    • B. Simon Maximal and minimal Schrödinger forms J. Operator Theory 1 1979 37-47
    • (1979) J. Operator Theory , vol.1 , pp. 37-47
    • Simon, B.1
  • 38
    • 85016600983 scopus 로고
    • Schrödinger semi-groups
    • B. Simon Schrödinger semi-groups Bull. Amer. Math. Soc. 7 1982 447-526
    • (1982) Bull. Amer. Math. Soc. , vol.7 , pp. 447-526
    • Simon, B.1
  • 39
    • 36149041879 scopus 로고
    • Theory of quantised Hall conductivity in two dimensions
    • P. Streda Theory of quantised Hall conductivity in two dimensions J. Phys. C 15 1982 L717-L721
    • (1982) J. Phys. C , vol.15
    • Streda, P.1
  • 42
    • 0031142034 scopus 로고    scopus 로고
    • Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential
    • W.-M. Wang Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential J. Funct. Anal. 146 1997 1-26
    • (1997) J. Funct. Anal. , vol.146 , pp. 1-26
    • Wang, W.-M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.