Statistics of resonances and of delay times in quasiperiodic Schrodinger equations

Physical Review Letters

Volumn 85, Issue 21, 2000, Pages 4426-4429

  Steinbach, F ^a   Ossipov, A ^a   Kottos, Tsampikos ^a   Geisel, T ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; CRYSTAL LATTICES; FRACTALS; MATHEMATICAL MODELS; METAL INSULATOR BOUNDARIES; RESONANCE; SPECTRUM ANALYSIS; STATISTICS; WAVE EQUATIONS;

HARPER MODEL; SCHRODINGER EQUATIONS;

QUANTUM THEORY;

EID: 0034323310     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.85.4426     Document Type: Article

References (40)

1. I. Rotter, Rep. Prog. Phys. 54, 635 (1991).
2. Atomic Spectra and Collisions in External Fields, edited by M. H. Nayfeh et al. (Plenum, New York, 1989), Vol. 2.
3. P. Gaspard, in Quantum Chaos, Proceedings of the International School of Physics "Enrico Fermi," edited by G. Casati et al. (North-Holland, Amsterdam, 1991), p. 307.
4. D. Stone, in Mesoscopic Quantum Physics, Proceedings of the Les Houches Summer, edited by E. Akkermans et al. (North-Holland, Amsterdam, 1991), pp. 373-433.
5. U. Smilansky, in Chaos and Quantum Physics, Proceedings of the Les Houches Summer School, edited by M.-J. Giannoni et al. (North-Holland, Amsterdam, 1989), pp. 371-441.
6. Tsampikos Kottos and Uzy Smilansky, Phys. Rev. Lett. 85, 968 (2000).
7. Y. V. Fyodorov and H.-J. Sommers, J. Math. Phys. 38, 1918 (1997).
8. P. W. Brouwer, K. M. Frahm, and C. W. Beenakker, Phys. Rev. Lett. 78, 4737 (1997).
9. A. D. Stone, D. C. Allan, and J. D. Joannopoulos, Phys. Rev. B 27, 836 (1983); Sandeep K. Joshi, Abhijit Kar Gupta, and A. M. Jayannavar, cond-mat/9712251.
10. A. D. Stone, D. C. Allan, and J. D. Joannopoulos, Phys. Rev. B 27, 836 (1983); Sandeep K. Joshi, Abhijit Kar Gupta, and A. M. Jayannavar, cond-mat/9712251.
11. A. M. Jayannavar, G. V. Vijayagovindan, and N. Kumar, Z. Phys. B 75, 77 (1989); J. Heinrichs, J. Phys. Condens. Matter 2, 1559 (1990); S. Anantha Ramakrishna and N. Kumar, cond-mat/9906098.
12. A. M. Jayannavar, G. V. Vijayagovindan, and N. Kumar, Z. Phys. B 75, 77 (1989); J. Heinrichs, J. Phys. Condens. Matter 2, 1559 (1990); S. Anantha Ramakrishna and N. Kumar, cond-mat/9906098.
13. A. M. Jayannavar, G. V. Vijayagovindan, and N. Kumar, Z. Phys. B 75, 77 (1989); J. Heinrichs, J. Phys. Condens. Matter 2, 1559 (1990); S. Anantha Ramakrishna and N. Kumar, cond-mat/9906098.
14. Christophe Texier and Alain Comtet, Phys. Rev. Lett. 82, 4220 (1999); C. J. Bolton-Heaton, C. J. Lambert, V. I. Falko, V. Prigodin, and A. J. Epstein, cond-mat/9902335.
15. Christophe Texier and Alain Comtet, Phys. Rev. Lett. 82, 4220 (1999); C. J. Bolton-Heaton, C. J. Lambert, V. I. Falko, V. Prigodin, and A. J. Epstein, cond-mat/9902335.
16. A. Ossipov, Tsampikos Kottos, and T. Geisel, Phys. Rev. B 61, 11 411 (2000).
17. M. Titov and C. Beenakker, cond-mat/0005042.
18. M. Titov and Van V. Fyodorov, Phys. Rev. B 61, R2444 (2000).
19. C. E. Porter, Statistical Theory of Spectral Fluctuations (Academic Press, New York, 1965).
20. T. Geisel, R. Ketzmerick, and G. Petschel, Phys. Rev. Lett. 66, 1651 (1991); in Quantum Chaos: Between Order and Disorder, edited by J. Casati and B. Chirikov (Cambridge University, Cambridge, England, 1995), pp. 634-659.
21. T. Geisel, R. Ketzmerick, and G. Petschel, Phys. Rev. Lett. 66, 1651 (1991); in Quantum Chaos: Between Order and Disorder, edited by J. Casati and B. Chirikov (Cambridge University, Cambridge, England, 1995), pp. 634-659.
22. P. G. Harper, Proc. R. Soc. London A 68, 874 (1955); S. Aubry and G. Andre, Ann. Isr. Phys. Soc. 3, 133 (1980); J. B. Sokolov, Phys. Rep. 126, 189 (1985); S. N. Evangelou and J.-L. Pichard, cond-mat/9902321.
23. P. G. Harper, Proc. R. Soc. London A 68, 874 (1955); S. Aubry and G. Andre, Ann. Isr. Phys. Soc. 3, 133 (1980); J. B. Sokolov, Phys. Rep. 126, 189 (1985); S. N. Evangelou and J.-L. Pichard, cond-mat/9902321.
24. P. G. Harper, Proc. R. Soc. London A 68, 874 (1955); S. Aubry and G. Andre, Ann. Isr. Phys. Soc. 3, 133 (1980); J. B. Sokolov, Phys. Rep. 126, 189 (1985); S. N. Evangelou and J.-L. Pichard, cond-mat/9902321.
25. P. G. Harper, Proc. R. Soc. London A 68, 874 (1955); S. Aubry and G. Andre, Ann. Isr. Phys. Soc. 3, 133 (1980); J. B. Sokolov, Phys. Rep. 126, 189 (1985); S. N. Evangelou and J.-L. Pichard, cond-mat/9902321.
26. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984); M. Kohmoto, L. P. Kadanoff, and C. Tang, Phys. Rev. Lett. 50, 1870 (1983); J. M. Luck and D. Petritis, J. Stat. Phys. 42, 289 (1986); J. Bellisard, B. Iochum, E. Scoppola, and D. Testard, Commun. Math. Phys. 125, 527 (1989).
27. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984); M. Kohmoto, L. P. Kadanoff, and C. Tang, Phys. Rev. Lett. 50, 1870 (1983); J. M. Luck and D. Petritis, J. Stat. Phys. 42, 289 (1986); J. Bellisard, B. Iochum, E. Scoppola, and D. Testard, Commun. Math. Phys. 125, 527 (1989).
28. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984); M. Kohmoto, L. P. Kadanoff, and C. Tang, Phys. Rev. Lett. 50, 1870 (1983); J. M. Luck and D. Petritis, J. Stat. Phys. 42, 289 (1986); J. Bellisard, B. Iochum, E. Scoppola, and D. Testard, Commun. Math. Phys. 125, 527 (1989).
29. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984); M. Kohmoto, L. P. Kadanoff, and C. Tang, Phys. Rev. Lett. 50, 1870 (1983); J. M. Luck and D. Petritis, J. Stat. Phys. 42, 289 (1986); J. Bellisard, B. Iochum, E. Scoppola, and D. Testard, Commun. Math. Phys. 125, 527 (1989).
30. P. Leboeuf, J. Kurchan, M. Feingold, and D. P. Arovas, Phys. Rev. Lett. 65, 3076 (1990); T. Geisel, R. Ketzmerick, and G. Petschel, Phys. Rev. Lett. 67, 3635 (1991); R. Artuso, F. Borgonovi, I. Guarneri, L. Rebuzzini, and G. Casati, Phys. Rev. Lett. 69, 3302 (1992).
31. P. Leboeuf, J. Kurchan, M. Feingold, and D. P. Arovas, Phys. Rev. Lett. 65, 3076 (1990); T. Geisel, R. Ketzmerick, and G. Petschel, Phys. Rev. Lett. 67, 3635 (1991); R. Artuso, F. Borgonovi, I. Guarneri, L. Rebuzzini, and G. Casati, Phys. Rev. Lett. 69, 3302 (1992).
32. P. Leboeuf, J. Kurchan, M. Feingold, and D. P. Arovas, Phys. Rev. Lett. 65, 3076 (1990); T. Geisel, R. Ketzmerick, and G. Petschel, Phys. Rev. Lett. 67, 3635 (1991); R. Artuso, F. Borgonovi, I. Guarneri, L. Rebuzzini, and G. Casati, Phys. Rev. Lett. 69, 3302 (1992).
33. C. Mahaux and H. A. Weidenmüller, Shell Model Approach in Nuclear Reactions (North-Holland, Amsterdam, 1969).
34. Y. Last, Commun. Math. Phys. 164, 421 (1994); R. Ketzmerick, K. Kruse, F. Steinbach, and T. Geisel, Phys. Rev. B 58, 9881 (1998).
35. Y. Last, Commun. Math. Phys. 164, 421 (1994); R. Ketzmerick, K. Kruse, F. Steinbach, and T. Geisel, Phys. Rev. B 58, 9881 (1998).
36. F. Borgonovi, I. Guarneri, and D. Shepelyansky, Phys. Rev. A 43, 4517 (1991).
37. 1.
38. F. Piéchon, Phys. Rev. Lett. 76, 4372 (1996).
39. F. M. Dittes, H. L. Harney, and A. Müller, Phys. Rev. A 45, 701 (1992).
40. A. Ossipov, F. Steinbach, Tsampikos Kottos, and T. Geisel (to be published).