Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators
Annales de l'I.H.P. Physique théorique, Tome 42 (1985) no. 4, pp. 383-406. 
@article{AIHPA_1985__42_4_383_0,
     author = {Kirsch, W. and Kotani, S. and Simon, B.},
     title = {Absence of absolutely continuous spectrum for some one dimensional random but deterministic {Schr\"odinger} operators},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {383--406},
     publisher = {Gauthier-Villars},
     volume = {42},
     number = {4},
     year = {1985},
     mrnumber = {801236},
     zbl = {0581.60052},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1985__42_4_383_0/}
}
TY  - JOUR
AU  - Kirsch, W.
AU  - Kotani, S.
AU  - Simon, B.
TI  - Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1985
SP  - 383
EP  - 406
VL  - 42
IS  - 4
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1985__42_4_383_0/
LA  - en
ID  - AIHPA_1985__42_4_383_0
ER  - 
%0 Journal Article
%A Kirsch, W.
%A Kotani, S.
%A Simon, B.
%T Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators
%J Annales de l'I.H.P. Physique théorique
%D 1985
%P 383-406
%V 42
%N 4
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1985__42_4_383_0/
%G en
%F AIHPA_1985__42_4_383_0
Kirsch, W.; Kotani, S.; Simon, B. Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators. Annales de l'I.H.P. Physique théorique, Tome 42 (1985) no. 4, pp. 383-406. http://archive.numdam.org/item/AIHPA_1985__42_4_383_0/

[1] J. Avron and B. Simon, Almost periodic Schrödinger operators, II. The integrated density of states, Duke Math. J., t. 50, 1983, p. 369-391. | MR | Zbl

[2] J. Bellissard, R. Lima and D. Testard, A metal-insulator transition for the almost Mathieu model, Commun. Math. Phys., t. 88, 1983, p. 207-234. | MR | Zbl

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

[4] V. De Alfaro and T. Regge, Potential Scattering, North Holland, Amsterdam, 1965. | MR | Zbl

[5] P. Deift and E. Trubowitz, Inverse Scattering on the Line, Comm. Pure Appl. Math., t. 32, 1979, p. 121-251. | MR | Zbl

[6] E. Dinaburg and Y. Sinai, On the one dimensional Schrödinger equation with quasi-periodic potential, Funk Anal. i Pril., t. 9, 1975, p. 8-21. | MR | Zbl

[7] I. Goldsheid, S. Molchanov and L. Pastur, A pure point spectrum of the stochastic and one dimensional Schrödinger equation, Funct. Anal. Appl., t. 11, 1977, p. 1-10. | MR | Zbl

[8] I. Herbst and J. Howland, The Stark ladder and other one-dimensional external field problems, Commun. Math. Phys., t. 80, 1981, p. 23. | MR | Zbl

[9] J. Keller, Discriminant, transmission coefficients and stability bands of Hill's equation, J. Math. Phys., to appear. | Zbl

[10] W. Kirsch, On a class of random Schrödinger operators, to appear in Adv. Appl. Math. | MR | Zbl

[11] W. Kirsch, F. Martinelli, On the spectrum of Schrödinger operators with a random potential: Commun. Math. Phys., t. 85, 1982, p. 329-350. | MR | Zbl

[12] W. Kirsch, F. Martinelli, On the ergodic properties of the spectrum of general random operators: J. Reine Angew. Math., t. 334, 1982, p. 141-156. | MR | Zbl

[13] S. Kotani, Lyaponov Indices Determine Absolutely Continuous Spectra of Stationary Random One-Dimensional Schrödinger Operators, Proc. Stoch. Anal., Kyoto, 1982. | Zbl

[14] S. Kotani, Support Theorems for Random Schrödinger Operators, Commun. Math. Phys., to appear. | MR | Zbl

[15] H. Kunz and B. Souillard, Sur le spectre des opérateurs aux différences finies aléatoires, Commun. Math. Phys., t. 78, 1980, p. 201-246. | MR | Zbl

[16] W. Magnus and S. Winkler, Hill's Equation, Interscience, 1966; Dover Edition available. | Zbl

[17] N. Mott and W. Twose, The theory of impurity conduction, Adv. in Physics, t. 10, 1961, p. 107-155.

[18] R. Newton, Inverse scattering by a local impurity in a periodic potential in one dimension. J. Math. Phys., t. 24, 1983, p. 2152. | MR | Zbl

[19] M. Reed and B. Simon, Methods of modern mathematical physics. III. Scattering theory, Academic Press, New York, 1979. | MR | Zbl

[20] M. Reed and B. Simon, Methods of modern mathematical physics. IV. Analysis of operators, Academic Press, New York, 1978. | MR | Zbl

[21] B. Simon, Kotani theory for one dimensional stochastic Jacobi matrices. Comm. Math. Phys., t. 89, 1983, p. 227. | MR | Zbl

[22] E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955. | MR | Zbl

[23] N. Dunford and J. Schwartz, Linear Operators, Vol. II, Wiley, New York, 1963. | MR | Zbl

[24] T. Kato, Schrödinger operators with singular potentials. Israel J. Math., t. 13, 1973, p. 135-148. | MR | Zbl

[25] W. Kirsch and F. Martinelli, On the essential selfadjointness of stochastic Schrödinger operators, Duke Math. J., t. 50, 1983, p. 1255-1260. | MR | Zbl