From power pure point to continuous spectrum in disordered systems

François Delyon; Barry Simon; Bernard Souillard

Annales de l'I.H.P. Physique théorique (1985)

  • Volume: 42, Issue: 3, page 283-309
  • ISSN: 0246-0211

How to cite

top

Delyon, François, Simon, Barry, and Souillard, Bernard. "From power pure point to continuous spectrum in disordered systems." Annales de l'I.H.P. Physique théorique 42.3 (1985): 283-309. <http://eudml.org/doc/76283>.

@article{Delyon1985,
author = {Delyon, François, Simon, Barry, Souillard, Bernard},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {random Schrödinger operators; power decaying eigenfunctions; Jacobi matrix; random potential},
language = {eng},
number = {3},
pages = {283-309},
publisher = {Gauthier-Villars},
title = {From power pure point to continuous spectrum in disordered systems},
url = {http://eudml.org/doc/76283},
volume = {42},
year = {1985},
}

TY - JOUR
AU - Delyon, François
AU - Simon, Barry
AU - Souillard, Bernard
TI - From power pure point to continuous spectrum in disordered systems
JO - Annales de l'I.H.P. Physique théorique
PY - 1985
PB - Gauthier-Villars
VL - 42
IS - 3
SP - 283
EP - 309
LA - eng
KW - random Schrödinger operators; power decaying eigenfunctions; Jacobi matrix; random potential
UR - http://eudml.org/doc/76283
ER -

References

top
  1. [1] D.J. Thouless, Percolation and Localization, in Ill-Condensed Matter Proceeding Les Houches, 1979, R. Balian, R. Maynard, G. Toulouse, editors, North-Holland, 1979. See also the reviews in Phys. Reports, t. 67, 1980. MR583170
  2. [2] B. Simon and B. Souillard, Franco-American Meeting on the Mathematics of Random and Almost Periodic Potentials, t. 36, p. 273-288, J. Stat. Phys., 1984. 
  3. [3] B. Souillard, Electrons in Random and Almost Periodic Potentials, Proceeding of the Workshop Common Trends in Particle and Condensed Matter Physics, Les Houches, 1983, Phys. Reports, t. 103, 1984, p. 41-46. MR839669
  4. [4] N.F. Mott and W.D. Twose, The Theory of Impurity Conduction, Adv. Phys., t. 10, 1961, p. 107-163. 
  5. [5] Y. Gold'sheid, S. Molchanov and L. Pastur, A pure Point Spectrum of the Stochastic and One-Dimensional Schrödinger Equation, Funct. Anal. i Pril., t. 11, 1977, p. 1-10; S. Molchanov, The Structure of Eigenfunctions of One-Dimensional Unordered Structures, Math. USSR Izv., t. 12, 1978, p. 69-101. MR470515
  6. [6] H. Kunz and B. Souillard, On the Spectrum of Random Finite Difference Operators, Commun. Math. Phys., t. 78, 1980, p. 201-246. Zbl0449.60048MR597748
  7. [7] R. Carmona, Exponential Localization in One-Dimensional Disordered Systems, Duke Math. J., t. 49, 1982, p. 191-213. Zbl0491.60058MR650377
  8. [8] G. Royer, Study of Schrödinger Operators with Random Potential in One-Dimension, Bull. Soc. Math., France, t. 110, 1982, p. 27-48. Zbl0523.60054MR662128
  9. [9] J. Lacroix, Problèmes probabilistes liés à l'étude des opérateurs aux différences finies aléatoires, Ann. de l'Institut Elie Cartan, n° 7, Nancy, 1982. Zbl0495.60068
  10. [10] F. Delyon, H. Kunz and B. Souillard, One Dimensional Wave Equation in Disordered Media, J. Phys., t. A 16, 1983, p. 25-42. Zbl0512.60052MR700179
  11. [11] H. Kunz and B. Souillard, The Localization Transition on the Bethe Lattice, J. Physique (Paris) Lettres, t. 44, 1983, p. 411, and to be published. 
  12. [12] B. Simon, Some Jacobi Matrices with Decaying Potential and Dense Point Spectrum, Commun. Math. Phys., t. 87, 1983, p. 253-258. Zbl0546.35048MR684102
  13. [13] 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., t. 88, 1983, p. 387-397. Zbl0531.60061MR701924
  14. [14] M. Ben-Artzj, An Application of Asymptotic Techniques to Certain Problems of Spectral and Scattering Theory of Stark-Like Hamiltonians, Trans. AMS, t. 278, 1983, p. 817-839; Unitary equivalence and scattering theory for Stark-like Hamiltonians, J. Math. Phys., t. 25, 1984, p. 951-964. Zbl0519.35064MR701525
  15. [15] V. Prigodin, One Dimensional Disordered System in an Electric Field, Sov. Phys. JETP, t. 52, 1980, p. 1185-1193. 
  16. [16] C.M. Soukoulis, J.V. José, E.N. Economou and Ping Sheng, Localization in One-Dimensional Disordered Systems in the Presence of an Electric Field, Phys. Rev. Lett., t. 50, 1983, p. 764-767. 
  17. [17] F. Delyon, B. Simon and B. Souillard, From Power Localized to Extended States in a Class of One-Dimensional Disordered Systems, Phys. Rev. Lett., t. 52, 1984, p. 2187. 
  18. [18] F. Bentosela, V. Grecchi and F. Zironi, Stark Wannier States in Disordered Systems, Marseille preprint, 1984. 
  19. [19] W. Craig and B. Simon, Subharmonicity of the Lyapunov Index, Duke Math. J., t. 50, 1983, p. 551-560. Zbl0518.35027MR705040
  20. [20] B. Simon, Functional Integration and Quantum Physics, Academic Press, 1979. Zbl0434.28013MR544188
  21. [21] L. Breiman, Probability, Addison-Wesley, 1968, proposition 5.13, p. 88. Zbl0174.48801MR229267
  22. [22] B. Derrida and E. Gardner, J. Physique (Paris), t. 45, 1984, p. 1283-1295. 
  23. [23] S. Kotani, Private Communication. 
  24. [24] R. Carmona, One Dimensional Schrödinger operators with random or deterministic Potentials: New Spectral Types, J. Funct. Anal., t. 51, 1983, p. 229-258. Zbl0516.60069MR701057

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.