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Volumn 146, Issue 2, 2001, Pages 365-398

Localization and universality of Poisson statistics for the multidimensional Anderson model at weak disorder

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EID: 0035629873     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220100169     Document Type: Article
Times cited : (36)

References (41)
  • 1
    • 0001324593 scopus 로고
    • Localization at weak disorder: Some elememtary bounds
    • M. Aizenman, Localization at weak disorder: some elememtary bounds, Rev. Math. Phys. 6 (1994), 1163
    • (1994) Rev. Math. Phys. , vol.6 , pp. 1163
    • Aizenman, M.1
  • 2
    • 24244444170 scopus 로고
    • Absence of diffusion in certain random lattices
    • P. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109 (1958), 1492
    • (1958) Phys. Rev. , vol.109 , pp. 1492
    • Anderson, P.1
  • 3
    • 0033727833 scopus 로고    scopus 로고
    • Constructive fractional-moment criteria for localization in random operators
    • M. Aizenman, R. Friedrich, D. Hundertmark, S. Shankar, Constructive fractional-moment criteria for localization in random operators, Phys. A279 (2000), 369-377
    • (2000) Phys. a , vol.279 , pp. 369-377
    • Aizenman, M.1    Friedrich, R.2    Hundertmark, D.3    Shankar, S.4
  • 4
    • 21344491724 scopus 로고
    • Localization at large disorder and at extreme energies: An elementary derivation
    • M. Aizenman, S. Molchanov, Localization at large disorder and at extreme energies: an elementary derivation, Commun. Math. Phys. 157 (1993), 245
    • (1993) Commun. Math. Phys. , vol.157 , pp. 245
    • Aizenman, M.1    Molchanov, S.2
  • 5
    • 0034381954 scopus 로고    scopus 로고
    • Correlation asymptotics of classical lattice spin systems with nonconvex Hamilton function at low temperature
    • V. Bach, T. Jecko, J. Sjöstrand, Correlation asymptotics of classical lattice spin systems with nonconvex Hamilton function at low temperature, Ann. Henri Poincaré 1 (2000), no. 1, 59-100
    • (2000) Ann. Henri Poincaré , vol.1 , Issue.1 , pp. 59-100
    • Bach, V.1    Jecko, T.2    Sjöstrand, J.3
  • 8
    • 0001643914 scopus 로고
    • Smoothness of the density of states in the Anderson model at high disorder
    • A. Bovier, M. Campanino, A. Klein, F. Perez, Smoothness of the density of states in the Anderson model at high disorder, Commun. Math. Phys. 114 (1988), 439-461
    • (1988) Commun. Math. Phys. , vol.114 , pp. 439-461
    • Bovier, A.1    Campanino, M.2    Klein, A.3    Perez, F.4
  • 10
    • 34249966896 scopus 로고
    • A new proof of localization in the Anderson tight binding model
    • 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
  • 11
    • 35549006412 scopus 로고
    • Statistical theory of energy levels of complex systems, I, II, III
    • F. Dyson, Statistical theory of energy levels of complex systems, I, II, III, J. Math. Phys. 3 (1962), 140-175
    • (1962) J. Math. Phys. , vol.3 , pp. 140-175
    • Dyson, F.1
  • 12
    • 0020498290 scopus 로고
    • Supersymmetry and the theory of disordered metals
    • K.B. Effetov, Supersymmetry and the theory of disordered metals, Adv. Phys. 32 (1983), 53-127
    • (1983) Adv. Phys. , vol.32 , pp. 53-127
    • Effetov, K.B.1
  • 13
    • 0030485972 scopus 로고    scopus 로고
    • Localization of classical waves I. Acoustic waves
    • 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
  • 14
  • 16
    • 0000284780 scopus 로고
    • Absence of diffusion in the Anderson tight binding model for large disorder or low energy
    • J. Fröhlich, T. Spencer, Absence of diffusion in the 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
  • 17
    • 84968508586 scopus 로고
    • Non commuting random products
    • H. Furstenberg, Non commuting random products, Trans. Amer. Soc. 108 (1963), 377-428
    • (1963) Trans. Amer. Soc. , vol.108 , pp. 377-428
    • Furstenberg, H.1
  • 18
    • 34250283162 scopus 로고
    • Pure point spectrum of stochastic one dimensional Schrödinger operators
    • Ya. Gol'dsheid, S. Molchanov, L. Pastur, Pure point spectrum of stochastic one dimensional Schrödinger operators, Func. Anal. Appl 11, 1 (1977), 1-10
    • (1977) Func. Anal. Appl , vol.11 , Issue.1 , pp. 1-10
    • Gol'dsheid, Y.1    Molchanov, S.2    Pastur, L.3
  • 20
    • 0038041007 scopus 로고    scopus 로고
    • On spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb inequality
    • J. Johnsen, On spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb inequality, Integral Equations Operator Theory 36 (2000), 288-324
    • (2000) Integral Equations Operator Theory , vol.36 , pp. 288-324
    • Johnsen, J.1
  • 21
    • 0001671617 scopus 로고
    • The supersymmetric replica trick and smoothness of the density of states for the random Schrödinger operators
    • 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), 315-331
    • (1990) Proceedings of Symposium in Pure Mathematics , vol.51 , pp. 315-331
    • Klein, A.1
  • 22
    • 0000791085 scopus 로고
    • Smmothness of the density of states in the Anderson model on a one-dimensional strip
    • A. Klein, A. Spies, Smmothness of the density of states in the Anderson model on a one-dimensional strip, Ann. Phys. 183 (1988), 352-398
    • (1988) Ann. Phys. , vol.183 , pp. 352-398
    • Klein, A.1    Spies, A.2
  • 26
    • 0030553788 scopus 로고    scopus 로고
    • Local fluctuation of the spectrum of a multidimensional Anderson tight binding model
    • N. Minami, Local fluctuation of the spectrum of a multidimensional Anderson tight binding model, Commun. Math. Phys. 177 (1996), 709-725
    • (1996) Commun. Math. Phys. , vol.177 , pp. 709-725
    • Minami, N.1
  • 27
    • 0002297290 scopus 로고
    • The structure of eigenfunctions of one-dimensional unordered structure
    • S.A. Molchanov, The structure of eigenfunctions of one-dimensional unordered structure, Math. USSR, Izv. 12 (1978), 69-101
    • (1978) Math. USSR, Izv. , vol.12 , pp. 69-101
    • Molchanov, S.A.1
  • 28
    • 5544291378 scopus 로고
    • The local structure of the spectrum of the one-dimensional Schrödinger operator
    • S.A. Molchanov, The local structure of the spectrum of the one-dimensional Schrödinger operator, Commun. Math. Phys. 78 (1981), 429-446
    • (1981) Commun. Math. Phys. , vol.78 , pp. 429-446
    • Molchanov, S.A.1
  • 31
    • 84990576488 scopus 로고
    • Singular continuous spectrum under rank one perturbation and localization for random Hamiltonians
    • B. Simon, T. Wolff, Singular continuous spectrum under rank one perturbation and localization for random Hamiltonians, Commun. Pure. Appl. Math XXXIX (1986), 75-90
    • (1986) Commun. Pure. Appl. Math , vol.39 , pp. 75-90
    • Simon, B.1    Wolff, T.2
  • 32
    • 0000793663 scopus 로고    scopus 로고
    • Correlation asymptotics and Witten Laplacians
    • J. Sjöstrand, Correlation asymptotics and Witten Laplacians, Algebra Anal. 8 (1996), 160-191
    • (1996) Algebra Anal. , vol.8 , pp. 160-191
    • Sjöstrand, J.1
  • 33
    • 4243557304 scopus 로고    scopus 로고
    • Complete asymptotics for correlations of Laplace integrals in the semi-classical limit
    • N.S.
    • J. Sjöstrand, Complete asymptotics for correlations of Laplace integrals in the semi-classical limit, Mém. Soc. Math. Fr. (N.S.) No. 83 (2000)
    • (2000) Mém. Soc. Math. Fr. , Issue.83
    • Sjöstrand, J.1
  • 34
    • 0033128444 scopus 로고    scopus 로고
    • Supersymmetric measures and maximum priciples in the complex domain-decay of Green's functions
    • J. Sjöstrand, W.M. Wang, Supersymmetric measures and maximum priciples in the complex domain-decay of Green's functions, Ann. Scient. Ec. Norm. Sup. 32 (1999), 347-414
    • (1999) Ann. Scient. Ec. Norm. Sup. , vol.32 , pp. 347-414
    • Sjöstrand, J.1    Wang, W.M.2
  • 35
    • 19544371356 scopus 로고
    • The Schrödinger equation with a random potential - A mathematical review
    • K. Osterwalder, R. Stora (eds.)
    • T. Spencer, The Schrödinger equation with a random potential - a mathematical review, Les Houches XLIII, K. Osterwalder, R. Stora (eds.) (1984)
    • (1984) Les Houches XLIII
    • Spencer, T.1
  • 38
    • 0003333881 scopus 로고
    • Geometric Integration Theory on Supermanifolds
    • USSR Academy of Sciences, Moscow
    • T. Voronov, Geometric Integration Theory on Supermanifolds, Mathematical Physics Review, USSR Academy of Sciences, Moscow 1993
    • (1993) Mathematical Physics Review
    • Voronov, T.1


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