From power pure point to continuous spectrum in disordered systems
Annales de l'I.H.P. Physique théorique, Tome 42 (1985) no. 3, pp. 283-309. 
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     title = {From power pure point to continuous spectrum in disordered systems},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {283--309},
     publisher = {Gauthier-Villars},
     volume = {42},
     number = {3},
     year = {1985},
     mrnumber = {797277},
     zbl = {0579.60056},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1985__42_3_283_0/}
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Delyon, François; Simon, Barry; Souillard, Bernard. From power pure point to continuous spectrum in disordered systems. Annales de l'I.H.P. Physique théorique, Tome 42 (1985) no. 3, pp. 283-309. http://archive.numdam.org/item/AIHPA_1985__42_3_283_0/

[1] D.J. Thouless, Percolation and Localization, in Ill-Condensed Matter Proceeding Les Houches, 1979, R. Balian, R. Maynard, G. Toulouse, editors, North-Holland, 1979. See also the reviews in Phys. Reports, t. 67, 1980. | MR

[2] B. Simon and B. Souillard, Franco-American Meeting on the Mathematics of Random and Almost Periodic Potentials, t. 36, p. 273-288, J. Stat. Phys., 1984.

[3] B. Souillard, Electrons in Random and Almost Periodic Potentials, Proceeding of the Workshop Common Trends in Particle and Condensed Matter Physics, Les Houches, 1983, Phys. Reports, t. 103, 1984, p. 41-46. | MR

[4] N.F. Mott and W.D. Twose, The Theory of Impurity Conduction, Adv. Phys., t. 10, 1961, p. 107-163.

[5] Y. Gold'Sheid, S. Molchanov and L. Pastur, A pure Point Spectrum of the Stochastic and One-Dimensional Schrödinger Equation, Funct. Anal. i Pril., t. 11, 1977, p. 1-10; S. Molchanov, The Structure of Eigenfunctions of One-Dimensional Unordered Structures, Math. USSR Izv., t. 12, 1978, p. 69-101. | MR

[6] H. Kunz and B. Souillard, On the Spectrum of Random Finite Difference Operators, Commun. Math. Phys., t. 78, 1980, p. 201-246. | MR | Zbl

[7] R. Carmona, Exponential Localization in One-Dimensional Disordered Systems, Duke Math. J., t. 49, 1982, p. 191-213. | MR | Zbl

[8] G. Royer, Study of Schrödinger Operators with Random Potential in One-Dimension, Bull. Soc. Math., France, t. 110, 1982, p. 27-48. | Numdam | MR | Zbl

[9] J. Lacroix, Problèmes probabilistes liés à l'étude des opérateurs aux différences finies aléatoires, Ann. de l'Institut Elie Cartan, n° 7, Nancy, 1982. | Zbl

[10] F. Delyon, H. Kunz and B. Souillard, One Dimensional Wave Equation in Disordered Media, J. Phys., t. A 16, 1983, p. 25-42. | MR | Zbl

[11] H. Kunz and B. Souillard, The Localization Transition on the Bethe Lattice, J. Physique (Paris) Lettres, t. 44, 1983, p. 411, and to be published.

[12] B. Simon, Some Jacobi Matrices with Decaying Potential and Dense Point Spectrum, Commun. Math. Phys., t. 87, 1983, p. 253-258. | MR | Zbl

[13] F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard and R. Weder, Schrödinger Operators with an Electric Field and Random or Deterministic Potentials. Commun. Math. Phys., t. 88, 1983, p. 387-397. | MR | Zbl

[14] M. Ben-Artzj, An Application of Asymptotic Techniques to Certain Problems of Spectral and Scattering Theory of Stark-Like Hamiltonians, Trans. AMS, t. 278, 1983, p. 817-839; Unitary equivalence and scattering theory for Stark-like Hamiltonians, J. Math. Phys., t. 25, 1984, p. 951-964. | MR | Zbl

[15] V. Prigodin, One Dimensional Disordered System in an Electric Field, Sov. Phys. JETP, t. 52, 1980, p. 1185-1193.

[16] C.M. Soukoulis, J.V. José, E.N. Economou and Ping Sheng, Localization in One-Dimensional Disordered Systems in the Presence of an Electric Field, Phys. Rev. Lett., t. 50, 1983, p. 764-767.

[17] F. Delyon, B. Simon and B. Souillard, From Power Localized to Extended States in a Class of One-Dimensional Disordered Systems, Phys. Rev. Lett., t. 52, 1984, p. 2187.

[18] F. Bentosela, V. Grecchi and F. Zironi, Stark Wannier States in Disordered Systems, Marseille preprint, 1984.

[19] W. Craig and B. Simon, Subharmonicity of the Lyapunov Index, Duke Math. J., t. 50, 1983, p. 551-560. | MR | Zbl

[20] B. Simon, Functional Integration and Quantum Physics, Academic Press, 1979. | MR | Zbl

[21] L. Breiman, Probability, Addison-Wesley, 1968, proposition 5.13, p. 88. | MR | Zbl

[22] B. Derrida and E. Gardner, J. Physique (Paris), t. 45, 1984, p. 1283-1295.

[23] S. Kotani, Private Communication.

[24] R. Carmona, One Dimensional Schrödinger operators with random or deterministic Potentials: New Spectral Types, J. Funct. Anal., t. 51, 1983, p. 229-258. | MR | Zbl