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Absence of diffusion in the Anderson tight binding model for large disorder or low energy. (English) Zbl 0519.60066

MSC:
60H25 Random operators and equations (aspects of stochastic analysis)
81P20 Stochastic mechanics (including stochastic electrodynamics)
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[1] Anderson, P.: Absence of diffusion in certain random lattices. Phys. Rev.109, 1492 (1958) · doi:10.1103/PhysRev.109.1492
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[3] Kunz, H., Souillard, B.: Sur le spectre des opérateurs aux différences finies aléatoires. Commun. Math. Phys.78, 201-246 (1980) · Zbl 0449.60048 · doi:10.1007/BF01942371
[4] Carmona, R.: Exponential localization in one-dimensional disordered systems. Duke Math. J.49, 191 (1982) · Zbl 0491.60058 · doi:10.1215/S0012-7094-82-04913-4
[5] Delyon, F., Kunz, H., Souillard, B.: One dimensional wave equation in disordered media. Preprint 1982, Ecole Polytechnique · Zbl 0512.60052
[6] Kunz, H., Souillard, B.: To appear
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[8] Fröhlich, J., Spencer, T.: The Kosterlitz-Thouless transition in two-dimensional abelian spin systems and the Coulomb gas. Commun. Math. Phys.81, 527 (1981); Kosterlitz-Thouless transition in two-dimensional plane rotator and Coulomb gas. Phys. Rev. Lett.46, 1006 (1981) · doi:10.1007/BF01208273
[9] Constantinescu, F., Fröhlich, J., Spencer, T.: To appear
[10] Wegner, F.: Bounds on the density of states in disordered systems. Z. Phys. B44, 9-15 (1981) · doi:10.1007/BF01292646
[11] McKane, A., Stone, M.: Localization as an alternative to Goldstone’s theorem. Ann. Phys.131, 36 (1981) · doi:10.1016/0003-4916(81)90182-2
[12] Ruelle, D.: A remark on bound states in potential-scattering theory. Nuovo Cimento A61, 655 (1969) · Zbl 0169.57502 · doi:10.1007/BF02819607
[13] Simon, B.: Correlation inequalities and the decay of correlations in ferromagnets. Commun. Math. Phys.77, 111 (1980) · doi:10.1007/BF01982711
[14] Edwards, S., Thouless, D.: Regularity of the density of states in Anderson’s localized electron model. J. Phys. C4, 453 (1971) · doi:10.1088/0022-3719/4/4/007
[15] Reed, M., Simon, B.: Methods of modern mathematical physics. IV. New York: Academic Press 1978 · Zbl 0401.47001
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