Random Schrödinger operators with a constant electric field
Minami, Nariyuki
Annales de l'I.H.P. Physique théorique, Tome 56 (1992), p. 307-344 / Harvested from Numdam
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Publié le : 1992-01-01
@article{AIHPA_1992__56_3_307_0,
     author = {Minami, Nariyuki},
     title = {Random Schr\"odinger operators with a constant electric field},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {56},
     year = {1992},
     pages = {307-344},
     mrnumber = {1160853},
     zbl = {0752.60052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1992__56_3_307_0}
}

Minami, Nariyuki. Random Schrödinger operators with a constant electric field. Annales de l'I.H.P. Physique théorique, Tome 56 (1992) pp. 307-344. http://gdmltest.u-ga.fr/item/AIHPA_1992__56_3_307_0/

[1] M. Ben-Artzi, Remarks on Schrödinger operators with an electric field and deterministic potentials, J. Math. Anal. Appl. Vol. 109, 1985, pp. 333-339. | MR 802899 | Zbl 0579.34018

[2] 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., Vol. 88, 1983, pp. 387-397. | MR 701924 | Zbl 0531.60061

[3] R. Carmona, Exponential localization in one dimensional disordered systems, Duke Math. J., Vol. 49, No. 1, 1982, pp. 191-213. | MR 650377 | Zbl 0491.60058

[4] R. Carmona, Exponential localization in one dimensional dosordered systems, Duke Math. J., Vol. 49, No. 1, 1982, pp. 191-213. | MR 650377 | Zbl 0491.60058

[4] E.T. Copson, Asymptotic expansions. Cambridge University Press, Cambridge, 1965. | MR 168979 | Zbl 0123.26001

[5] F. Delyon, B. Simon and B. Souillard, From power pure point to continuous spectrum in disordered systems. Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 42, No. 3, 1985, pp. 283-309. | Numdam | MR 797277 | Zbl 0579.60056

[6] D.J. Gilbert and D.B. Pearson, On subordinacy and analysis of spectrum of one-dimensional Schrödinger operators, J. Math. Anal. Appl., Vol. 128, 1987, pp. 30-56. | MR 915965 | Zbl 0666.34023

[7] D.J. Gilbert, On subordinacy and analysis of Schrödinger operators with two singular endpoints. Proc. R. Soc. Edinburg, Vol. 112A, 1989, pp. 213-229. | Zbl 0678.34024

[8] I.Ya. Goldsheid, S.A. Molchanov and L.A. Pastur, A pure point spectrum of the stochastic one-dimensional Schrödinger operator, Funct. Anal. Appl., Vol. 11, No. 1, 1977, pp. 1-8. | Zbl 0368.34015

[9] Ph. Hartman, Differential equations with non-oscillatory eigenfunctions, Duke Math. J., Vol. 15, 1948, pp. 697-709. | MR 27927 | Zbl 0031.30606

[10] Ph. Hartman, A characterization of the spectra of one-dimensional wave equations, Am. J. Math., Vol. 71, 1949, pp. 915-920. | MR 33419 | Zbl 0035.18303

[11] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland/Kodansha, 1981. | MR 637061 | Zbl 0495.60005

[12] K. Ito and H.P. Mckean, Diffusion processes and their sample paths, Springer, Berlin, 1965. | Zbl 0127.09503

[13] S. Kotani, Lyapounov exponents and spectra for one-dimensional random Schrödinger operators, Contemporary Math., Vol. 50, 1985, pp. 277-286. | MR 841099 | Zbl 0587.60054

[14] S. Kotani and B. Simon, Localization in general one-dimensional random systems. II. Continuum Schrödinger operators, Commun. Math. Phys., Vol. 112, 1987, pp. 103- 119. | MR 904140 | Zbl 0637.60080

[15] N. Minami, Schrödinger operator with potential which is the derivative of a temporally homogeneous Lévy process. Probability and mathematical statistics. Fifth JapanU.S.S.R. symposium proceedings, Lect. Notes Math., 1299, 1986, pp. 298-304. | MR 936002 | Zbl 0636.60068

[16] N. Minami, Exponential and super-exponential localizations for one-dimensional Schrödinger operators with Lévy noise potentials. Tsukuba J. Math., Vol. 13, No. 1, 1989, pp. 225-282. | MR 1003604 | Zbl 0694.60058

[17] S.A. Molchanov, The structure of eigenfunctions of one-dimensional unordered structures, Math. U.S.S.R. Izv., Vol. 12, No. 1, 1978, pp. 69-101. | Zbl 0401.34023