Stark resonances for random potentials of Anderson type

F. Bentosela; P. Briet

Annales de l'I.H.P. Physique théorique (1999)

  • Volume: 71, Issue: 5, page 497-538
  • ISSN: 0246-0211

How to cite

top

Bentosela, F., and Briet, P.. "Stark resonances for random potentials of Anderson type." Annales de l'I.H.P. Physique théorique 71.5 (1999): 497-538. <http://eudml.org/doc/76843>.

@article{Bentosela1999,
author = {Bentosela, F., Briet, P.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {random potentials of Anderson type; Schrödinger operator; disorder systems; Stark-Wainner resonances; spectral properties; Hamiltonian; electron moving in a random potential; exterior constant electric field; coupling constants; resolvent operator; analytical distortion method},
language = {eng},
number = {5},
pages = {497-538},
publisher = {Gauthier-Villars},
title = {Stark resonances for random potentials of Anderson type},
url = {http://eudml.org/doc/76843},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Bentosela, F.
AU - Briet, P.
TI - Stark resonances for random potentials of Anderson type
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 71
IS - 5
SP - 497
EP - 538
LA - eng
KW - random potentials of Anderson type; Schrödinger operator; disorder systems; Stark-Wainner resonances; spectral properties; Hamiltonian; electron moving in a random potential; exterior constant electric field; coupling constants; resolvent operator; analytical distortion method
UR - http://eudml.org/doc/76843
ER -

References

top
  1. [1] V.J. Asch and P. Briet, Lower bounds on the width of Stark-Wannier type resonances, Commun. Math. Phys.179 (1996) 725-735. Zbl0851.34078MR1400760
  2. [2] J. Asch, P. Exner and P. Duclos, Stark-Wannier Hamiltonian with pure point spectrum, in: Proc. of Conf. on Diff. Equat. Postdam (1996). Zbl0883.47007
  3. [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. Zbl0531.60061MR701924
  4. [4] F. Bentosela and V. Grecchi, Stark-Wannier ladders, Commun. Math. Phys.142 (1991) 169-192. Zbl0743.35053MR1137778
  5. [5] P. Briet, Les résonances de forme, Thèse de doct. d'Etat, Univ. Toulon et du Var, 1995. 
  6. [6] P. Briet, J.M. Combes and P. Duclos, Spectral stability under tunnelling, Commun. Math. Phys.126 (1989) 133-156. Zbl0702.35189MR1027916
  7. [7] P. Briet and E. Mourre, Some resolvent estimates for Sturm Liouville operators, J. Math. Anal. Appl.201 (1996) 867-879. Zbl0863.34083MR1400568
  8. [8] P. Bougerol and J. Lacroix, Products of Random Matrices with Applications to Random Shrödinger Operators, Birkhäuser, Boston, 1985. Zbl0572.60001MR886674
  9. [9] V.S. Buslaev and L.A. Dimitrieva, Bloch-electron in an external field, Leningrad Math. J.1 (1990) 287-320. Zbl0726.34070
  10. [10] R. Carmona and J. Lacroix, Spectral Theory of Random Shrödinger Operators, Birkhäuser, Boston, 1990. Zbl0717.60074MR1102675
  11. [11] J.M. Combes, P. Hislop, Stark ladder resonances for small electric field, Commun. Math. Phys.140 (1991) 291-320. Zbl0737.34060MR1124271
  12. [12] J.M. Combes and P. Hislop, Localization for some continuous random Hamiltonian in d-dimension, J. Funct. Anal.124 (1994) 149-180. Zbl0801.60054MR1284608
  13. [13] Ju.L. Dalesckii and M.G. Krein, Stability of Solutions of Differential Equations in Banach Space, Trans. Math. Mono. 43, 1974. MR352639
  14. [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). Zbl0908.47002
  15. [15] F. Delyon, B. Souillard and B. Simon, From pure point to continuous spectrum in disordered systems, Ann. Inst. Henri Poincaré42 (3) (1985) 283-309. Zbl0579.60056MR797277
  16. [16] P. Exner, The Absence of the absolutely continuous spectrum for δ' Wannier Stark Ladders, J. Math. Phys.36 (9) (1995) 4561-4570. Zbl0884.47049MR1347099
  17. [17] V. Grecchi, M. Maioli and A. Sacchetti, Stark resonances in disordered systems, Commun. Math. Phys.146 (1992) 231-240. Zbl0770.47030MR1165181
  18. [18] B. Helffer and J. Sjöstrand, Puits multiples dans la limite semi classique I, Comm. in P.D.E.9 (1984) 337-408. Zbl0546.35053
  19. [19] I. Herbst and J. Howland, The Stark ladder and other one-dimensional external electric field, Commun. Math. Phys.140 (1981) 23-42. Zbl0473.47037MR623150
  20. [20] P. Hislop and I.M. Sigal, Semi classical theory of shape resonances in quantum mechanics, Memoirs Amer. Math. Soc.399 (1989). Zbl0704.35115
  21. [21] W. Hunziker, Distortion analyticity and molecular resonance curve, Ann. Inst. Poincaré45 (1986) 339-358. Zbl0619.46068MR880742
  22. [22] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966. Zbl0148.12601MR407617
  23. [23] S. Kotani and B. Simon, Localisation in general one-dimensional random systems, Commun. Math. Phys.112 (1987). Zbl0637.60080
  24. [24] F. Martinelli and E. Scoppola, Introduction to the mathematical theory of Anderson localisation, La Revista del Nuovo Cimento10 (3) (1987). MR924528
  25. [25] E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Commun. Math. Phys.78 (1981) 391-408. Zbl0489.47010MR603501
  26. [26] L. Pastur and A. Figotin, Spectra of Random and Almost-Periodic Operators, Springer, Berlin, 1992. Zbl0752.47002MR1223779
  27. [27] M. Reed and B. Simon, Methods of Modern Mathematical Physics IV: Analysis of Operators, Academic Press, New York, 1978. Zbl0401.47001MR493421
  28. [28] B. Simon, Spectral analysis of rank one perturbations and applications, in: CDM Proc. Lecture Notes 8, 1995, pp. 109-149. Zbl0824.47019MR1332038
  29. [29] G. Stolz, Localization for random Schrödinger operators with poisson potentials, Ann. Inst. Henri Poincare63 (3) (1995) 297-314. Zbl0843.60058MR1363537

NotesEmbed ?

top

You must be logged in to post comments.