Spectral statistics in chaotic systems with a point interaction

Journal of Physics A: Mathematical and General

Volumn 33, Issue 36, 2000, Pages 6263-6278

  Sieber, Martin ^a  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034664378     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/36/301     Document Type: Article

References (25)

1. Hannay J H and Ozorio de Almeida A M 1984 Periodic orbits and a correlation function for the semiclassical density of states J. Phys. A: Math. Gen. 17 3429-40
2. Berry M V 1985 Semiclassical theory of spectral rigidity Proc. R. Soc. A 400 229-51
3. Bogomolny E B and Keating J P 1996 Gutzwiller's trace formula and spectral statistics: beyond the diagonal approximation Phys. Rev. Lett. 77 1472-5
4. Bohigas O 1991 Random matrix theories and chaotic dynamics Les Houches 1989 Session LII on Chaos and Quantum Physics ed M J Giannoni, A Voros and J Zinn-Justin (Amsterdam: North-Holland) pp 87-199
5. Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
6. Argaman N, Dittes F, Doron E, Keating J, Kitaev A, Sieber M and Smilansky U 1993 Correlations in the actions of periodic orbits derived from quantum chaos Phys. Rev. Lett. 71 4326-9
7. Bohigas O, Giannoni M J and Schmit C 1984 Characterization of chaotic quantum spectra and universality of level fluctuation laws Phys. Rev. Lett. 52 1-4
8. Sieber M 1999 Geometrical theory of diffraction and spectral statistics J. Phys. A: Math. Gen. 32 7679-89
9. Albeverio S, Gesztesy F, Høegh-Krohn R and Holden H 1988 Solvable Models in Quantum Mechanics (New York: Springer)
10. Vattay G, Wirzba A and Rosenqvist P E 1994 Periodic orbit theory of diffraction Phys. Rev. Lett. 73 2304-7
11. Pavloff N and Schmit C 1995 Diffractive orbits in quantum billiards Phys. Rev. Lett. 75 61-4 Pavloff N and Schmit C Phys. Rev. Lett. 75 3779 (erratum)
12. Bruus H and Whelan N D 1996 Edge diffraction, trace formulae and the cardioid billiard Nonlinearity 9 1023-47
13. Rosenqvist P E, Vattay G and Wirzba A 1996 Application of the diffraction trace formula to the three-disk scattering system J. Stat. Phys. 83 243-57
14. Dahlqvist P and Vattay G 1998 Periodic orbit quantization of the Sinai billiard in the small scatterer limit J. Phys. A: Math. Gen. 31 6333-45
15. Dahlqvist P 1999 From chaotic to disordered systems - a periodic orbit approach J. Phys. A: Math. Gen. 32 725-38
16. Exner P and Seba P 1996 Point interactions in two and three dimensions as models of small scatterers Phys. Lett. A 222 1-4
17. Fishman S and Keating J P 1998 The diagonal approximation for non-time-reversal-symmetric systems J. Phys. A: Math. Gen. 31 L313-9
18. Simons B D and Altshuler B L 1993 Universalities in the spectra of disordered and chaotic systems Phys. Rev. B 48 5422-38
19. Sieber M 2000 in preparation
20. Eckhardt B, Fishman S, Keating J, Agam O, Main J and Müller K 1995 Approach to ergodicity in quantum wave functions Phys. Rev. E 52 5893-903
21. de Carvalho T O, Keating J P and Robbins J M 1998 Fluctuations in quantum expectation values for chaotic systems with broken time-reversal symmetry J. Phys. A: Math. Gen. 31 5631-40
22. Leboeuf P and Sieber M 1999 Universality in quantum parametric correlations Phys. Rev. E 60 3969-72
23. Ozorio de Almeida A M, Lewenkopf C H and Mucciolo E R 1998 Semiclassical limit of universal parametric density correlations Phys. Rev. E 58 5693-703
24. + for the one-channel case J. Phys. A: Math. Gen. 31 3439-48
25. Bogomolny E B, Leboeuf P and Schmit C 2000 Spectral statistics of chaotic systems with a point-like scatterer Preprint nlin. CD/0003016