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Volumn 13, Issue 6, 2003, Pages 1201-1238

Explicit finite volume criteria for localization in continuous random media and applications

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EID: 1142264344     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-003-0444-5     Document Type: Article
Times cited : (52)

References (52)
  • 1
    • 21344491724 scopus 로고
    • Localization at large disorder and extreme energies: An elementary derivation
    • [AM]
    • [AM] M. AIZENMAN, S. MOLCHANOV, Localization at large disorder and extreme energies: an elementary derivation. Commun. Math. Phys. 157 (1993), 245-278.
    • (1993) Commun. Math. Phys. , vol.157 , pp. 245-278
    • Aizenman, M.1    Molchanov, S.2
  • 4
    • 0007130625 scopus 로고    scopus 로고
    • Landau Hamiltonians with unbounded random potentials
    • [BCH]
    • [BCH] J.M. BARBAROUX, J.M. COMBES, P.D. HISLOP, Landau Hamiltonians with unbounded random potentials, Lett. Math. Phys. 40 (1997), 355-369.
    • (1997) Lett. Math. Phys. , vol.40 , pp. 355-369
    • Barbaroux, J.M.1    Combes, J.M.2    Hislop, P.D.3
  • 5
    • 0002362803 scopus 로고
    • Anderson localization for Bernoulli and other singular potentials
    • [CKM]
    • [CKM] R. CARMONA, A. KLEIN, F. MARTINELLI, Anderson localization for Bernoulli and other singular potentials, Commun. Math. Phys. 108 (1987), 41-66.
    • (1987) Commun. Math. Phys. , vol.108 , pp. 41-66
    • Carmona, R.1    Klein, A.2    Martinelli, F.3
  • 6
    • 0001026869 scopus 로고
    • Localization for some continuous, random Hamiltonian in d-dimension
    • [CoH1]
    • [CoH1] J.M. COMBES, P.D. HISLOP, Localization for some continuous, random Hamiltonian in d-dimension, J. Funct. Anal. 124 (1994), 149-180.
    • (1994) J. Funct. Anal. , vol.124 , pp. 149-180
    • Combes, J.M.1    Hislop, P.D.2
  • 7
    • 0000059896 scopus 로고    scopus 로고
    • Landau Hamiltonians with random potentials: Localization and the density of states
    • [CoH2]
    • [CoH2] J.M. COMBES, P.D. HISLOP, Landau Hamiltonians with random potentials: localization and the density of states, Commun. Math. Phys. 177 (1996), 603-629.
    • (1996) Commun. Math. Phys. , vol.177 , pp. 603-629
    • Combes, J.M.1    Hislop, P.D.2
  • 8
    • 0035531720 scopus 로고    scopus 로고
    • p-theory of the spectral shift function, the Wegner estimate and the integrated density of states for some random operators
    • [CoHN]
    • p-theory of the spectral shift function, the Wegner estimate and the integrated density of states for some random operators, Commun. Math. Phys. 218 (2001), 113-130.
    • (2001) Commun. Math. Phys. , vol.218 , pp. 113-130
    • Combes, J.M.1    Hislop, P.D.2    Nakamura, S.3
  • 9
    • 0036475771 scopus 로고    scopus 로고
    • The Wegner estimate and the integrated density of states for some random operators
    • [CoHKN]
    • [CoHKN] J.M. COMBES, P.D. HISLOP, F. KLOPP, S. NAKAMURA, The Wegner estimate and the integrated density of states for some random operators, Proc. Indian Acad. Sci. (Math. Sci.) 112 (2002), 31-53.
    • (2002) Proc. Indian Acad. Sci. (Math. Sci.) , vol.112 , pp. 31-53
    • Combes, J.M.1    Hislop, P.D.2    Klopp, F.3    Nakamura, S.4
  • 10
    • 0000951121 scopus 로고    scopus 로고
    • Band edge localization and the density of states for acoustic and electromagnetic waves in random media
    • [CoHT]
    • [CoHT] J.M. COMBES, P.D. HISLOP, A. TIP, Band edge localization and the density of states for acoustic and electromagnetic waves in random media, Ann. Inst. H. Poincaré Phys. Theor. 70 (1999), 381-428.
    • (1999) Ann. Inst. H. Poincaré Phys. Theor. , vol.70 , pp. 381-428
    • Combes, J.M.1    Hislop, P.D.2    Tip, A.3
  • 11
    • 0035634523 scopus 로고    scopus 로고
    • Multi-scale analysis implies strong dynamical localization, GAFA
    • [DS]
    • [DS] D. DAMANIK, P. STOLLMANN, Multi-scale analysis implies strong dynamical localization, GAFA, Geom. funct. anal. 11 (2001), 11-29.
    • (2001) Geom. Funct. Anal. , vol.11 , pp. 11-29
    • Damanik, D.1    Stollmann, P.2
  • 12
    • 0031138777 scopus 로고    scopus 로고
    • The Nature of the spectrum for the Landau Hamiltonian with delta impurities
    • [DoMP1]
    • [DoMP1] T.C. DORLAS, N. MAORIS, J.V. PULÉ, The Nature of the spectrum for the Landau Hamiltonian with delta impurities, J. Stat. Phys. 87 (1997), 847-875.
    • (1997) J. Stat. Phys. , vol.87 , pp. 847-875
    • Dorlas, T.C.1    Maoris, N.2    Pulé, J.V.3
  • 13
    • 0033241786 scopus 로고    scopus 로고
    • Characterization of the spectrum of the Landau Hamiltonian with delta impurities
    • [DoMP2]
    • [DoMP2] T.C. DORLAS, N. MAORIS, J.V. PULÉ, Characterization of the spectrum of the Landau Hamiltonian with delta impurities, Commun. Math. Phys. 204 (1999), 367-396.
    • (1999) Commun. Math. Phys. , vol.204 , pp. 367-396
    • Dorlas, T.C.1    Maoris, N.2    Pulé, J.V.3
  • 15
    • 34249966896 scopus 로고
    • A new proof of localization in the Anderson tight binding model
    • [DrK1]
    • [DrK1] H. VON DREIFUS, A. KLEIN, A new proof of localization in the Anderson tight binding model. Commun. Math. Phys. 124 (1989), 285-299.
    • (1989) Commun. Math. Phys. , vol.124 , pp. 285-299
    • Von Dreifus, H.1    Klein, A.2
  • 16
    • 0007163722 scopus 로고
    • Localization for random Schrodinger operators with correlated potentials
    • [DrK2]
    • [DrK2] H. VON DREIFUS, A. KLEIN, Localization for random Schrodinger operators with correlated potentials, Commun. Math. Phys. 140 (1991), 133-147.
    • (1991) Commun. Math. Phys. , vol.140 , pp. 133-147
    • Von Dreifus, H.1    Klein, A.2
  • 17
    • 21344494130 scopus 로고
    • Localization phenomenon in gaps of the spectrum of random lattice operators
    • [FK1]
    • [FK1] A. FIGOTlN, A. KLEIN, Localization phenomenon in gaps of the spectrum of random lattice operators, J. Stat. Phys. 75 (1994), 997-1021.
    • (1994) J. Stat. Phys. , vol.75 , pp. 997-1021
    • Figotln, A.1    Klein, A.2
  • 18
    • 21844492784 scopus 로고
    • Localization of electromagnetic and acoustic waves in random media. Lattice model
    • [FK2]
    • [FK2] A. FIGOTIN. A. KLEIN, Localization of electromagnetic and acoustic waves in random media. Lattice model, J. Stat. Phys. 76 (1994), 985-1003.
    • (1994) J. Stat. Phys. , vol.76 , pp. 985-1003
    • Figotin, A.1    Klein, A.2
  • 19
    • 0030485972 scopus 로고    scopus 로고
    • Localization of classical waves I: Acoustic waves
    • [FK3]
    • [FK3] A. FIGOTIN. A. KLEIN, Localization of classical waves I: Acoustic waves, Commun. Math. Phys. 180 (1996), 439-482.
    • (1996) Commun. Math. Phys. , vol.180 , pp. 439-482
    • Figotin, A.1    Klein, A.2
  • 20
    • 0031534447 scopus 로고    scopus 로고
    • Localization of classical waves II: Electromagnetic waves
    • [FK4]
    • [FK4] A. FIGOTIN, A. KLEIN, Localization of classical waves II: Electromagnetic waves, Commun. Math. Phys. 184 (1997), 411-441.
    • (1997) Commun. Math. Phys. , vol.184 , pp. 411-441
    • Figotin, A.1    Klein, A.2
  • 21
    • 0034549703 scopus 로고    scopus 로고
    • Spectral localization by Gaussian random potentials in multi-dimensional continuous space
    • [FiLM]
    • [FiLM] W. FISCHER, H. LESCHKE, P. MÜLLER, Spectral localization by Gaussian random potentials in multi-dimensional continuous space, J. Statist. Phys. 101 (2000), 935-985.
    • (2000) J. Statist. Phys. , vol.101 , pp. 935-985
    • Fischer, W.1    Leschke, H.2    Müller, P.3
  • 22
    • 0002119217 scopus 로고
    • Constructive proof of localization in the Anderson tight binding model
    • [FrMSS]
    • [FrMSS] J. FRÖHLICH. F. MARTINELLI, E. SCOPPOLA, T. SPENCER, Constructive proof of localization in the Anderson tight binding model, Commun. Math. Phys. 101 (1985), 21-46.
    • (1985) Commun. Math. Phys. , vol.101 , pp. 21-46
    • Fröhlich, J.1    Martinelli, F.2    Scoppola, E.3    Spencer, T.4
  • 23
    • 0000284780 scopus 로고
    • Absence of diffusion with Anderson tight binding model for large disorder or low energy
    • [FrS]
    • [FrS] J. FRÖHLICH, T. SPENCER, Absence of diffusion with Anderson tight binding model for large disorder or low energy, Commun. Math. Phys. 88 (1983), 151-184.
    • (1983) Commun. Math. Phys. , vol.88 , pp. 151-184
    • Fröhlich, J.1    Spencer, T.2
  • 24
    • 0040163789 scopus 로고    scopus 로고
    • Dynamical localization for discrete and continuous random Schrödinger operators
    • [GD]
    • [GD] F. GERMINET, S. DE BIÈVRE, Dynamical localization for discrete and continuous random Schrödinger operators, Commun. Math. Phys. 194 (1998), 323-341.
    • (1998) Commun. Math. Phys. , vol.194 , pp. 323-341
    • Germinet, F.1    De Bièvre, S.2
  • 25
    • 0035538238 scopus 로고    scopus 로고
    • Bootstrap multiscale analysis and localization in random media
    • [GK1]
    • [GK1] 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
  • 26
    • 0037374309 scopus 로고    scopus 로고
    • Decay of operator-valued kernels of functions of Schrodinger and other operators
    • [GK2]
    • [GK2] F. GERMINET, A. KLEIN, Decay of operator-valued kernels of functions of Schrodinger and other 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
  • 27
    • 4644231405 scopus 로고    scopus 로고
    • A characterization of the Anderson metalinsulator transport transition
    • [GK3], to appear
    • [GK3] F. GERMINET, A. KLEIN, A characterization of the Anderson metalinsulator transport transition, Duke Math. J., to appear.
    • Duke Math. J.
    • Germinet, F.1    Klein, A.2
  • 28
    • 1142310346 scopus 로고    scopus 로고
    • High disorder localization for random Schrödinger operators through explicit finite volume criteria. Markov Process
    • [GK4], to appear
    • [GK4] F. GERMINET, A. KLEIN, High disorder localization for random Schrödinger operators through explicit finite volume criteria. Markov Process. Related Fields, to appear.
    • Related Fields
    • Germinet, F.1    Klein, A.2
  • 29
    • 1142286094 scopus 로고    scopus 로고
    • The Anderson metal-insulator transport transition
    • [GK5], to appear
    • [GK5] F. GERMINET, A. KLEIN, The Anderson metal-insulator transport transition, Contemporary Mathematics, to appear.
    • Contemporary Mathematics
    • Germinet, F.1    Klein, A.2
  • 30
    • 34250283162 scopus 로고
    • Pure point spectrum of stochastic one dimensional Schrödinger operators
    • [GoMP]
    • [GoMP] YA. GOL'DSHEID, S. MOLCHANOV, L. PASTUR, Pure point spectrum of stochastic one dimensional Schrödinger operators, Funct. Anal. Appl. 11 (1977), 1-10.
    • (1977) Funct. Anal. Appl. , vol.11 , pp. 1-10
    • Gol'dsheid, Ya.1    Molchanov, S.2    Pastur, L.3
  • 31
  • 32
    • 0037145490 scopus 로고    scopus 로고
    • The integrated density of states for some random operators with nonsign definite potentials
    • [HK]
    • [HK] P.D. HISLOP, F. KLOPP, The integrated density of states for some random operators with nonsign definite potentials, J. Funct. Anal. 195 (2002), 1247.
    • (2002) J. Funct. Anal. , vol.195 , pp. 1247
    • Hislop, P.D.1    Klopp, F.2
  • 33
    • 0000196301 scopus 로고
    • On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator
    • [HoM]
    • [HoM] H. HOLDEN, F. MARTINELLI, On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator, Commun. Math. Phys. 93 (1984), 197-217.
    • (1984) Commun. Math. Phys. , vol.93 , pp. 197-217
    • Holden, H.1    Martinelli, F.2
  • 34
    • 0030093716 scopus 로고    scopus 로고
    • Wegner estimates and localization for alloy-type potentials
    • [K]
    • [K] W. KIRSCH, Wegner estimates and localization for alloy-type potentials, Math. Zeit. 221 (1996), 507-512.
    • (1996) Math. Zeit. , vol.221 , pp. 507-512
    • Kirsch, W.1
  • 35
    • 0001207353 scopus 로고
    • On the spectrum of Schrödinger operators with a random potential
    • [KM]
    • [KM] W. KIRSCH, F. MARTINELLI, On the spectrum of Schrödinger operators with a random potential, Commun. Math. Phys. 85 (1982), 329-350.
    • (1982) Commun. Math. Phys. , vol.85 , pp. 329-350
    • Kirsch, W.1    Martinelli, F.2
  • 36
    • 84868025903 scopus 로고    scopus 로고
    • Localization for random perturbations of periodic Schrödinger operators
    • [KSS1]
    • [KSS1] W. KIRSCH, P. STOLLMAN, G. STOLZ, Localization for random perturbations of periodic Schrödinger operators, Random Oper. Stochastic Equations 6 (1998), 241-268.
    • (1998) Random Oper. Stochastic Equations , vol.6 , pp. 241-268
    • Kirsch, W.1    Stollman, P.2    Stolz, G.3
  • 37
    • 0040350235 scopus 로고    scopus 로고
    • Anderson localization for random Schrödinger operators with long range interactions
    • [KSS2]
    • [KSS2] W. KIRSCH, P. STOLLMAN, G. STOLZ, Anderson localization for random Schrödinger operators with long range interactions, Commun. Math. Phys. 195 (1998), 495-507.
    • (1998) Commun. Math. Phys. , vol.195 , pp. 495-507
    • Kirsch, W.1    Stollman, P.2    Stolz, G.3
  • 38
    • 0001123780 scopus 로고
    • Localization in the Anderson model with long range hopping
    • [Kl1]
    • [Kl1] A. KLEIN, Localization in the Anderson model with long range hopping, Brazilian Journal of Physics 23 (1993), 363-371.
    • (1993) Brazilian Journal of Physics , vol.23 , pp. 363-371
    • Klein, A.1
  • 39
    • 0343879832 scopus 로고    scopus 로고
    • Localization of light in randomized periodic media
    • [Kl2] (J.-P. Fouque, ed.), Kluwer. The Netherlands
    • [Kl2] A. KLEIN, Localization of light in randomized periodic media, in "Diffuse Waves in Complex Media" (J.-P. Fouque, ed.), Kluwer. The Netherlands (1999), 73-92.
    • (1999) Diffuse Waves in Complex Media , pp. 73-92
    • Klein, A.1
  • 40
    • 0001875208 scopus 로고    scopus 로고
    • A general framework for localization of classical waves: I. Inhomogeneous media and defect eigenmodes
    • [KlK1]
    • [KlK1] A. KLEIN, A. KOINES, A general framework for localization of classical waves: I. Inhomogeneous media and defect eigenmodes, Math. Phys. Anal. Geom. 4 (2001), 97-130.
    • (2001) Math. Phys. Anal. Geom. , vol.4 , pp. 97-130
    • Klein, A.1    Koines, A.2
  • 41
    • 3543068115 scopus 로고    scopus 로고
    • A general framework for localization of classical waves: II. Random media
    • [KlK2], in press
    • [KlK2] A. KLEIN, A. KOINES, A general framework for localization of classical waves: II. Random media, Math. Phys. Anal. Geom., in press (2003).
    • (2003) Math. Phys. Anal. Geom.
    • Klein, A.1    Koines, A.2
  • 42
    • 38249018247 scopus 로고
    • Localization for the Anderson model on a strip with singular potentials
    • [KlLS]
    • [KlLS] A. KLEIN. J. LACROIX. A. SPEIS, Localization for the Anderson model on a strip with singular potentials, J. Punct. Anal. 94 (1990), 135-155.
    • (1990) J. Punct. Anal. , vol.94 , pp. 135-155
    • Klein, A.1    Lacroix, J.2    Speis, A.3
  • 43
    • 21844521255 scopus 로고
    • Localization for continuous random Schrödinger operators
    • [Klo1]
    • [Klo1] F. KLOPP, Localization for continuous random Schrödinger operators, Commun. Math. Phys. 167 (1995), 553-569.
    • (1995) Commun. Math. Phys. , vol.167 , pp. 553-569
    • Klopp, F.1
  • 44
    • 0036882746 scopus 로고    scopus 로고
    • Weak disorder localization and Lifshitz tails
    • [Klo2]
    • [Klo2] F. KLOPP, Weak disorder localization and Lifshitz tails, Commun. Math. Phys. 232 (2002), 125-155.
    • (2002) Commun. Math. Phys. , vol.232 , pp. 125-155
    • Klopp, F.1
  • 45
    • 0036025587 scopus 로고    scopus 로고
    • Weak disorder localization and Lifshitz tails: Continuous Hamiltonians
    • [Klo3]
    • [Klo3] F. KLOPP, Weak disorder localization and Lifshitz tails: continuous Hamiltonians, Ann. I.H.P. 3 (2002), 711-737.
    • (2002) Ann. I.H.P. , vol.3 , pp. 711-737
    • Klopp, F.1
  • 46
    • 34250250635 scopus 로고
    • Spectral properties of disordered systems in one-body approximation
    • [P]
    • [P] L. PASTUR, Spectral properties of disordered systems in one-body approximation, Commun. Math. Phys. 75 (1980), 179-196.
    • (1980) Commun. Math. Phys. , vol.75 , pp. 179-196
    • Pastur, L.1
  • 47
    • 85016600983 scopus 로고
    • Schrödinger semi-groups
    • [S]
    • [S] 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
  • 48
    • 0000083362 scopus 로고
    • Localization for random and quasiperiodic potentials
    • [Sp]
    • [Sp] T. SPENCER, Localization for random and quasiperiodic potentials, J. Stat. Phys. 51 (1988), 1009-1019.
    • (1988) J. Stat. Phys. , vol.51 , pp. 1009-1019
    • Spencer, T.1
  • 51
    • 0031142034 scopus 로고    scopus 로고
    • Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential
    • [W1]
    • [W1] 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
  • 52
    • 0035629873 scopus 로고    scopus 로고
    • Localization and universality of Poisson statistics for the multidimensional Anderson model at weak disorder
    • [W2]
    • [W2] W.M. WANG, Localization and universality of Poisson statistics for the multidimensional Anderson model at weak disorder, Invent. Math. 146 (2001), 365-398.
    • (2001) Invent. Math. , vol.146 , pp. 365-398
    • Wang, W.M.1


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