Localization for random Schrödinger operators with Poisson potential

Günter Stolz

Annales de l'I.H.P. Physique théorique (1995)

  • Volume: 63, Issue: 3, page 297-314
  • ISSN: 0246-0211

How to cite

top

Stolz, Günter. "Localization for random Schrödinger operators with Poisson potential." Annales de l'I.H.P. Physique théorique 63.3 (1995): 297-314. <http://eudml.org/doc/76697>.

@article{Stolz1995,
author = {Stolz, Günter},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {random Schrödinger operator; localization; eigenfunction},
language = {eng},
number = {3},
pages = {297-314},
publisher = {Gauthier-Villars},
title = {Localization for random Schrödinger operators with Poisson potential},
url = {http://eudml.org/doc/76697},
volume = {63},
year = {1995},
}

TY - JOUR
AU - Stolz, Günter
TI - Localization for random Schrödinger operators with Poisson potential
JO - Annales de l'I.H.P. Physique théorique
PY - 1995
PB - Gauthier-Villars
VL - 63
IS - 3
SP - 297
EP - 314
LA - eng
KW - random Schrödinger operator; localization; eigenfunction
UR - http://eudml.org/doc/76697
ER -

References

top
  1. [1] R. Carmona, One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types, J. Funct. Anal., Vol. 51, 1983, pp. 229-258. Zbl0516.60069MR701057
  2. [2] R. Carmonara and J. Lacroix, Spectral theory of random Schrödinger operators, Birkhäuser, Basel-Berlin, 1990. Zbl0717.60074MR1102675
  3. [3] E.A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. Zbl0064.33002MR69338
  4. [4] J.-M. Combes and P.D. Hislop, Localization for continuous random Hamiltonians in d-dimensions, J. Funct. Anal., Vol. 124, 1994, pp. 149-180. Zbl0801.60054MR1284608
  5. [5] R. Del Rio, N. Makarov and B. Simon, Operators with singular continuous spectrum, II. Rank one operators, Commun. Math. Phys., Vol. 165, 1994, pp. 59-67. Zbl1055.47500MR1298942
  6. [6] R. Del Rio, B. Simon and G. Stolz, Stability of spectral types for Sturm-Liouville operators, Math. Research Lett., Vol. 1, 1994, pp. 437-450. Zbl0838.34090MR1302387
  7. [7] J.L. Doob, Stochastic Processes, Wiley, New York, 1953. Zbl0053.26802MR58896
  8. [8] A. Gordon, Pure point spectrum under 1-parameter perturbations and instability of Anderson localization, Commun. Math. Phys., Vol. 164, 1994, pp. 489-506. Zbl0839.47002MR1291242
  9. [9] Ph. Hartman, The number of L2-solutions of x'' + q (t) x = 0, Amer. J. Math., Vol. 73, 1951, pp. 635-645. Zbl0044.31202MR44695
  10. [10] I.W. Herbst, J.S. Howland, The Stark ladder and other one-dimensional extemal field problems, Commun. Math. Phys., Vol. 80, 1981, pp. 23-42. Zbl0473.47037MR623150
  11. [11] P.D. Hilsop, S. Nkamura, Stark Hamiltonians with unbounded random potentials, Rev. Math. Phys., Vol. 2, 1990, pp. 479-494. Zbl0727.34076MR1107687
  12. [12] O. Kallenberg, Random Measures, Akademie-Verlag, Berlin, 1975. Zbl0345.60031MR431372
  13. [13] J.F.C. Kingman, Poisson Processes, Clarendon Press, Oxford, 1993. Zbl0771.60001MR1207584
  14. [14] W. Kirsch, S. Kotani and B. Simon, Absence of absolutely continuous spectrum for some one dimensional random but deterministic potentials, Ann. Inst. Henri Poincaré, Vol. 42, 1985, pp. 383-406. Zbl0581.60052MR801236
  15. [15] W. Kirsch, S.A. Molchanov and L.A. Pastur, One-dimensional Schrödinger operator with unbounded potential: The pure point spectrum, Funct. Anal. Appl., Vol. 24, 1990, pp. 176-186. Zbl0747.47023MR1082027
  16. [16] W. Kirsch, S.A. Molchanov and L.A. Pastur, One-dimensional Schrödinger operator with high potential barriers, Operator Theory: Advances and Applications, Vol. 57, pp. 163-170, Birkhäuser-Verlag, 1992. Zbl0883.34078MR1230898
  17. [17] F. Klopp, Localization for Semiclassical Continuous Random Schrödinger Operators II: the Random Displacement Model, Helv. Phys. Acta, Vol. 66, 1993, pp. 810-841. Zbl0820.60043MR1264047
  18. [18] S. Kotani, Lyapunov indices determine absolute contnuous spectra of stationnary one dimensional Schrödinger operators, Proc. Taneguchi Intern. Symp. on Stochastic Analysis, Katata and Kyoto, 1982, pp. 225-247, North Holland, 1983. Zbl0549.60058MR780760
  19. [19] S. Kotani, Lyapunov exponents and spectra for one-dimensional Schrödinger operators, Contemp. Math., Vol. 50, 1986, pp. 277-286. Zbl0587.60054
  20. [20] S. Kotani and B. Simon, Localization in General One-Dimensional Random Systems, Commun. Math. Phys., Vol. 112, 1987, pp. 103-119. Zbl0637.60080MR904140
  21. [21] N. Minami, Exponential and Super-Exponential Localizations for One-Dimensional Schrödinger Operators with Lévy Noise Potentials, Tsukuba J. Math., Vol. 13, 1989, pp. 225-282. Zbl0694.60058MR1003604
  22. [22] L. Pastur and A. Figotin, Spectra of Random and Almost-Periodic Operators, Springer-Verlag, 1991. Zbl0752.47002MR1223779
  23. [23] Th Poerschke, G. Stolz and J. Weidmann, Expansions in Generalized Eigenfunctions of Selfadjoint Operators, Math. Z., Vol. 202, 1989, pp. 397-408. Zbl0661.47021MR1017580
  24. [24] B. Simon, Trace ideals and their Applications, Cambridge University Press, Cambridge, 1979. Zbl0423.47001MR541149
  25. [25] B. Simon, Schrödinger semigroups, Bull. Am. Math. Soc., Vol. 7, 1982, pp. 447-526. Zbl0524.35002MR670130
  26. [26] B. Simon, Localization in General One Dimensional Random Systems, I. Jacobi Matrices, Commun. Math. Phys., Vol. 102, 1985, pp. 327-336. Zbl0604.60062MR820578
  27. [27] B. Simon and T. Wolff, Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Commun. Pure Appl. Math., Vol. 39, 1986, pp. 75-90. Zbl0609.47001MR820340
  28. [28] G. Stolz, Note to the paper by P.D. Hilsop and S. Nakamura: Stark Hamiltonian with unbounded random potentials, Rev. Math. Phys., Vol. 5, 1993, pp. 453-456. Zbl0782.34088MR1223529
  29. [29] G. Stolz, Spectral theory of Schrödinger operators with potentials of infinite barriers type, Habilitationsschrift, Frankfurt, 1994. Zbl0819.34049
  30. [30] G. Stolz, Localization for the Poisson model, in "Spectral Analysis and Partial Differential Equations", Operator Theory: Advances and Applications, Vol. 78, pp. 375-380, Birkhäuser-Verlag, 1955. Zbl0841.34089MR1365351
  31. [31] J. Weidmann, Spectral Theory of Ordinary Differential Operators, Lect. Notes in Math., Vol. 1258, Springer/Verlag, 1987. Zbl0647.47052MR923320

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.