Spectral statistics of a quantum interval-exchange map

Physical Review Letters

Volumn 93, Issue 25, 2004, Pages

  Bogomolny, E ^a   Schmit, C ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL PROBLEMS; QUANTIZATION; QUANTUM INTERVAL-EXCHANGE MAPS; SPECTRAL STATISTICS;

COMPRESSIBILITY; CORRELATION METHODS; EIGENVALUES AND EIGENFUNCTIONS; MAPS; MATHEMATICAL MODELS; MATRIX ALGEBRA; POISSON DISTRIBUTION; SPECTRUM ANALYSIS;

QUANTUM THEORY;

EID: 42749102212     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.93.254102     Document Type: Article

References (16)

1. M. L. Mehta, Random Matrices (Academic Press, New York, 1991), 2nd ed.
2. T. Prosen and M. Robnik, J. Phys. A 27, 8059 (1994).
3. I. Dumitriu and A. Edelman, J. Math. Phys. (N.Y.) 43, 5830 (2002).
4. O. Giraud, J. Marklof, and S. O'Keefe, J. Phys. A 37, L303 (2004).
5. 2 was considered but the answer depends strongly on arithmetic nature of N due to special properties of the Gauss sums.
6. E. Bogomolny, U. Gerland, and C. Schmit, Eur. Phys. J. B 19, 121 (2001).
7. E. Bogomolny, U. Gerland, and C. Schmit, Phys. Rev. E 59, 1315(R) (1999).
8. Higher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill, New York, London, Toronto, 1955), Vol. 3, p. 206.
9. E. Bogomolny and C. Schmit (to be published).
10. S. Albeverio et al., Solvable Models in Quantum Mechanics (Springer, New York, 1988).
11. k are ignored.
12. M. V. Berry and M. Tabor, Proc. R. Soc. London 356, 375 (1977).
13. k together form the super-Poisson sequence [9].
14. H. Hernández-Saltaña, J. Flores, and T. H. Seligman, Phys. Rev. E 60, 449 (1999).
15. Other cases are less drastic and will be considered elsewhere [9].
16. Semi-Poisson results χ = 1/n and 2/n for, respectively, nonsymmetric and symmetric matrices agree with the computation of χ from periodic orbits as in [4].