Stark resonances for random potentials of Anderson type
Annales de l'I.H.P. Physique théorique, Volume 71 (1999) no. 5, p. 497-538
@article{AIHPA_1999__71_5_497_0,
     author = {Bentosela, Fran\c cois and Briet, P.},
     title = {Stark resonances for random potentials of Anderson type},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {71},
     number = {5},
     year = {1999},
     pages = {497-538},
     zbl = {0955.47044},
     mrnumber = {1728190},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1999__71_5_497_0}
}
Bentosela, F.; Briet, P. Stark resonances for random potentials of Anderson type. Annales de l'I.H.P. Physique théorique, Volume 71 (1999) no. 5, pp. 497-538. http://www.numdam.org/item/AIHPA_1999__71_5_497_0/

[1] V.J. Asch and P. Briet, Lower bounds on the width of Stark-Wannier type resonances, Commun. Math. Phys. 179 (1996) 725-735. | MR 1400760 | Zbl 0851.34078

[2] J. Asch, P. Exner and P. Duclos, Stark-Wannier Hamiltonian with pure point spectrum, in: Proc. of Conf. on Diff. Equat. Postdam (1996). | Zbl 0883.47007

[3] F. Bentosela, R. Carmona, P. Duclos, B. Souillard, B. Simon and R. Weder, Shrödinger operators with an electric field and random or deterministic potential, Commun. Math. Phys. 88 (1983) 333-339. | MR 701924 | Zbl 0531.60061

[4] F. Bentosela and V. Grecchi, Stark-Wannier ladders, Commun. Math. Phys. 142 (1991) 169-192. | MR 1137778 | Zbl 0743.35053

[5] P. Briet, Les résonances de forme, Thèse de doct. d'Etat, Univ. Toulon et du Var, 1995.

[6] P. Briet, J.M. Combes and P. Duclos, Spectral stability under tunnelling, Commun. Math. Phys. 126 (1989) 133-156. | MR 1027916 | Zbl 0702.35189

[7] P. Briet and E. Mourre, Some resolvent estimates for Sturm Liouville operators, J. Math. Anal. Appl. 201 (1996) 867-879. | MR 1400568 | Zbl 0863.34083

[8] P. Bougerol and J. Lacroix, Products of Random Matrices with Applications to Random Shrödinger Operators, Birkhäuser, Boston, 1985. | MR 886674 | Zbl 0572.60001

[9] V.S. Buslaev and L.A. Dimitrieva, Bloch-electron in an external field, Leningrad Math. J. 1 (1990) 287-320. | Zbl 0726.34070

[10] R. Carmona and J. Lacroix, Spectral Theory of Random Shrödinger Operators, Birkhäuser, Boston, 1990. | MR 1102675 | Zbl 0717.60074

[11] J.M. Combes, P. Hislop, Stark ladder resonances for small electric field, Commun. Math. Phys. 140 (1991) 291-320. | MR 1124271 | Zbl 0737.34060

[12] J.M. Combes and P. Hislop, Localization for some continuous random Hamiltonian in d-dimension, J. Funct. Anal. 124 (1994) 149-180. | MR 1284608 | Zbl 0801.60054

[13] Ju.L. Dalesckii and M.G. Krein, Stability of Solutions of Differential Equations in Banach Space, Trans. Math. Mono. 43, 1974. | MR 352639 | Zbl 0286.34094

[14] R. Del Rio, S. Jitomirskaya, Y. Last and B. Simon, Operators with singular continuous spectrum IV: Haudsorff dimension, rank one perturbations and localisation, to be submitted in Bull. Amer. Math. Soc. (1996). | Zbl 0908.47002

[15] F. Delyon, B. Souillard and B. Simon, From pure point to continuous spectrum in disordered systems, Ann. Inst. Henri Poincaré 42 (3) (1985) 283-309. | Numdam | MR 797277 | Zbl 0579.60056

[16] P. Exner, The Absence of the absolutely continuous spectrum for δ' Wannier Stark Ladders, J. Math. Phys. 36 (9) (1995) 4561-4570. | MR 1347099 | Zbl 0884.47049

[17] V. Grecchi, M. Maioli and A. Sacchetti, Stark resonances in disordered systems, Commun. Math. Phys. 146 (1992) 231-240. | MR 1165181 | Zbl 0770.47030

[18] B. Helffer and J. Sjöstrand, Puits multiples dans la limite semi classique I, Comm. in P.D.E. 9 (1984) 337-408. | Zbl 0546.35053

[19] I. Herbst and J. Howland, The Stark ladder and other one-dimensional external electric field, Commun. Math. Phys. 140 (1981) 23-42. | MR 623150 | Zbl 0473.47037

[20] P. Hislop and I.M. Sigal, Semi classical theory of shape resonances in quantum mechanics, Memoirs Amer. Math. Soc. 399 (1989). | Zbl 0704.35115

[21] W. Hunziker, Distortion analyticity and molecular resonance curve, Ann. Inst. Poincaré 45 (1986) 339-358. | Numdam | MR 880742 | Zbl 0619.46068

[22] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966. | MR 407617 | Zbl 0148.12601

[23] S. Kotani and B. Simon, Localisation in general one-dimensional random systems, Commun. Math. Phys. 112 (1987). | Zbl 0637.60080

[24] F. Martinelli and E. Scoppola, Introduction to the mathematical theory of Anderson localisation, La Revista del Nuovo Cimento 10 (3) (1987). | MR 924528

[25] E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Commun. Math. Phys. 78 (1981) 391-408. | MR 603501 | Zbl 0489.47010

[26] L. Pastur and A. Figotin, Spectra of Random and Almost-Periodic Operators, Springer, Berlin, 1992. | MR 1223779 | Zbl 0752.47002

[27] M. Reed and B. Simon, Methods of Modern Mathematical Physics IV: Analysis of Operators, Academic Press, New York, 1978. | MR 493421 | Zbl 0401.47001

[28] B. Simon, Spectral analysis of rank one perturbations and applications, in: CDM Proc. Lecture Notes 8, 1995, pp. 109-149. | MR 1332038 | Zbl 0824.47019

[29] G. Stolz, Localization for random Schrödinger operators with poisson potentials, Ann. Inst. Henri Poincare 63 (3) (1995) 297-314. | Numdam | MR 1363537 | Zbl 0843.60058