Spectral statistics of a pseudo-integrable map: The general case

Nonlinearity

Volumn 22, Issue 9, 2009, Pages 2101-2126

  Bogomolny, E ^a   Dubertrand, R ^a,b   Schmit, C ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68849127367     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/22/9/003     Document Type: Article

References (21)

1. Berry M and Tabor M 1977 Level clustering in the regular spectrum Proc. R. Soc. Lond. A 356 375
2. Bohigas O, Giannoni M-J and Schmit C 1984 Characterization of chaotic quantum spectra and universality of level fluctuation laws Phys. Rev. Lett. 52 1
3. Bogomolny E, Georgeot B, Giannoni M-J and Schmit C 1997 Arithmetical chaos Phys. Rep. 291 220
4. Richens P J and Berry M V 1981 Pseudointegrable systems in classical and quantum mechanics Physica D: Nonlinear Phenom. 2 495
5. Zemlyakov A N and Katok A B 1975 Topological transitivity in billiards in polygons Math. Notes 18 760
6. Bogomolny E, Gerland U and Schmit C 1999 Models of intermediate spectral statistics Phys. Rev. E 59 R1315
7. Shklovskii B I, Shapiro B, Sears B R, Lambrianides P and Shore H B 1993 Statistics of spectra of disordered systems near the metal-insulator transition Phys. Rev. B 47 11487
8. Evers F and Mirlin A D 2008 Anderson transitions Rev. Mod. Phys. 80 1355
9. Bogomolny E, Giraud O and Schmit C 2001 Periodic orbits contribution to the 2-point correlation form factor for pseudo-integrable systems Commun. Math. Phys. 222 327
10. Sommerfeld A 1954 Optics (New York: Academic)
11. Bogomolny E and Schmit C 2004 Structure of wave functions of pseudointegrable billiards Phys. Rev. Lett. 92 244102
12. Bogomolny E, Dietz B, Friedrich T, Miski-Oglu M and Richter A 2006 Phys. Rev. Lett. 97 254102
13. Giraud O, Marklof J and O'Keefe S 2004 Intermediate statistics in quantum maps J. Phys. A: Math. Gen. 37 L303
14. Marklof J and Rudnick Z 2000 Quantum unique ergodicity for parabolic map Geom. Funct. Anal. 10 1554
15. Bogomolny E and Schmit C 2004 Spectral statistics of a quantum interval-exchange map Phys. Rev. Lett. 93 254102
16. Mehta M L 2004 Random Matrices (New York: Academic)
17. Bogomolny E, Gerland U and Schmit C 2001 Short range plasma models for intermediate spectral statistics Eur. Phys. J. B 19 121
18. Albeverio S, Gesztesy F, Hoegh-Krohn R and Holgen H 1988 Solvable Models in Quantum Mechanics (New York: Springer)
19. Bogomolny E, Giraud O and Schmit C 2009 Random matrix ensembles associated with Lax matrices Phys. Rev. Lett. submitted arXiv:nlin.0904.4898
20. Karlin S and McGregor J 1959 Coincidence probabilities Pacific J. Math. 9 1141
21. Martin M, Giraud O and Georgeot B 2008 Multifractality and intermediate statistics in quantum maps Phys. Rev. E 77 035201