Spectral properties and anomalous transport in a polygonal billiard

Chaos

Volumn 10, Issue 1, 2000, Pages 189-194

  Artuso, Roberto ^a   Guarneri, Italo ^a   Rebuzzini, Laura ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034147001     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166493     Document Type: Article

References (17)

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2. P. R. Halmos, Lectures on Ergodic Theory (Chelsea, New York, 1955).
3. I. Guarneri, "On the dynamical meaning of spectral dimensions," Ann. Inst. Henri Poincare 68, 491 (1998), and references therein.
4. R. Artuso, G. Casati, and I. Guarneri, "Numerical study on ergodic properties of triangular billiards," Phys. Rev. E 55, 1 (1997).
5. E. Gutkin, "Billiards in polygons," Physica D 19, 311 (1986).
6. E. Gutkin, "Billiards in polygons: survey of recent results," J. Stat. Phys. 83, 7 (1996).
7. Such a filtering procedure does not affect results pertaining to B and C classes.
8. F. J. Harris, "On the use of windows for harmonic analysis with the discrete Fourier transform," Proc. IEEE 66, 51 (1978).
9. Further details about the procedure are described in Ref. 4 (see also Ref. 12, where this technique has been applied to the analysis of kicked quantum systems).
10. I. Guarneri and H. Schulz-Baldes, "Lower bounds on wave packet by packing dimensions of spectral measures," to appear in Electron. J. Math. Phys.
11. R. Ketzmerick, G. Petschel, and T. Geisel, "Slow decay of temporal correlations in quantum systems with Cantor spectra," Phys. Rev. Lett. 69, 695 (1992); M. Holschneider, "Fractal wavelet dimensions and localization," Commun. Math. Phys. 160, 457 (1994).
12. R. Ketzmerick, G. Petschel, and T. Geisel, "Slow decay of temporal correlations in quantum systems with Cantor spectra," Phys. Rev. Lett. 69, 695 (1992); M. Holschneider, "Fractal wavelet dimensions and localization," Commun. Math. Phys. 160, 457 (1994).
13. R. Artuso, D. Belluzzo, and G. Casati, "Thermodynamic analysis of the spectral measure for kicked quantum system," Europhys. Lett. 25, 181 (1994).
14. 2(t)/log(t)] this definition has the advantage of ignoring all kinds of subdominant contributions.
15. H. Schulz-Baldes and J. Bellissard, "Anomalous transport: a mathematical framework," Rev. Math. Phys. 10, 1 (1998).
16. A. Hof, "On scaling in relation to singular spectra," Commun. Math. Phys. 184, 567 (1997).
17. As a matter of fact, absolute continuity of the spectrum implies the strong mixing property (see Ref. 1).