On the distribution of matrix elements for the quantum cat map

Annals of Mathematics

Volumn 161, Issue 1, 2005, Pages 489-507

  Kurlberg, Pär ^a   Rudnick, Zeév ^b  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23744437056     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2005.161.489     Document Type: Article

References (18)

1. E. BOMBIERI, On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71-105.
2. Y. COLIN DE VERDIÈRE, Ergodicité et fonctions propres du laplacien, Comm. Math. Phys. 102 (1985), 497-502.
3. M. DEGLI ESPOSTI, Quantization of the orientation preserving automorphisms of the torus, Ann. Inst. H. Poincaré Phys. Théor. 58 (1993), 323-341.
4. M. DEGLI ESPOSTI, S. GRAFFI, and S. ISOLA, Classical limit of the quantized hyperbolic toral automorphisms, Comm. Math. Phys. 167 (1995), 471-507.
5. B. ECKHARDT, S. FISHMAN, J. KEATING, O. AGAM, J. MAIN, and K. MÜLLER, Approach to ergodicity in quantum wave functions, Phys. Rev. E 52 (1995), 5893-5903.
6. F. FAURE, S. NONNENMACHER, and S. DE BIÈVRE, Scarred eigenstates for quantum cat maps of minimal periods, Comm. Math. Phys. 29 (2003), 449-492.
7. M. FEINGOLD and A. PERES, Distribution of matrix elements of chaotic systems, Phys. Rev. A 34 (1986), 591-595.
8. J. H. HANNAY and M. V. BERRY, Quantization of linear maps on a torus-Fresnel diffraction by a periodic grating, Phys. D 1 (1980), 267-290.
9. P. KURLBERG, A local Riemann hypothesis. II, Math. Z. 233 (2000), 21-37.
10. P. KURLBERG and Z. RUDNICK, Hecke theory and equidistribution for the quantization of linear maps of the torus, Duke Math. J. 103 (2000), 47-77.
11. _, Value distribution for eigenfunctions of desymmetrized quantum maps, Internat. Math. Res. Not. (2001), No. 18 985-1002.
12. W. Z. Luo and P. SARNAK, Quantum invariance for Hecke eigenforms, Ann. Sci. École Norm. Sup. (4) 37 (2004), 769-799.
13. F. MEZZADRI, On the multiplicativity of quantum cat maps, Nonlinearity 15 (2002), 905-922.
14. P. SARNAK, Spectra of hyperbolic surfaces, Bull. Amer. Math. Soc. 40 (2003) 441-478 (electronic).
15. A. I. SCHNIRELMAN, Ergodic properties of eigenfunctions. Uspkehi Mat. Nauk 29 (1974), 181-182.
16. T. WATSON, Rankin triple products and quantum chaos, Ph.D. thesis, Princeton University, 2003.
17. S. ZELDITCH, Uniform distribution of eigenfunctions on compact hyperbolic surfaces. Duke Math. J. 55 (1987), 919-941.
18. _, Quantum ergodicity of C* dynamical systems, Comm. Math. Phys. 177 (1996), 507-528.