Quick Search:
Prog. Theor. Phys. Vol. 110 No. 3 (2003) pp. 499-516
Correlation Analysis of Quantum Fluctuations and Repulsion Effects of Classical Dynamics in SU(3) model
Shigeyasu Fujiwara* and
Fumihiko Sakata**
Department of Mathematical Sciences, Ibaraki University, Mito 310-8512, Japan
(Received December 4, 2002)
Abstract:
In many quantum systems, random matrix theory has been used to
characterize quantum level fluctuations, which is known to be a
quantum correspondent to a regular-to-chaos transition in
classical systems. We present a new qualitative analysis of quantum and
classical fluctuation properties by exploiting correlation
coefficients and variances. It is shown that the correlation
coefficient of the quantum level density is
roughly inversely proportional relation to the
variance of consecutive phase-space point spacings on the
Poincaré section plane.
URL :
http://ptp.ipap.jp/link?PTP/110/499/
DOI : 10.1143/PTP.110.499
References:
- M. L. Mehta, Random matrices, 2nd ed. (Academic Press, 1991).
-
T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandy and S. S. M. Wong, Rev. Mod. Phys. 53 (1981), 385[APS].
-
T. Terasaka and T. Matsushita, Phys. Rev. A 32 (1985), 538[APS].
-
A. Shudo and N. Saitô, J. Phys. Soc. Jpn. 56 (1987), 2641[JPSJ].
-
H. Friedrich and D. Wintgen, Phys. Rep. 183 (1989), 37[CrossRef].
- A. Bohr and B. R. Mottelson, Nuclear Structure I (Benjamin, New York, 1969).
-
T. Guhr, A. Müller-Groeling and H. A. Weidenmüller, Phys. Rep. 299 (1998), 189[CrossRef].
-
S. Y. Li, A. Klein and R. M. Dreizler, J. Math. Phys. 11 (1970), 975[CrossRef].
- T. Marumori, T. Maskawa, F. Sakata and A. Kuriyama, Prog. Theor. Phys. 64 (1980), 1294[PTP].
- F. Sakata, T. Marumori, Y. Hashimoto and T. Une, Prog. Theor. Phys. 70 (1983), 424[PTP].
-
H. Yoshida, Phys. Lett. A 150 (1990), 262[CrossRef].
- A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, Applied Mathematical Sciences, 38 (Springer, Berlin, 1983).
- K. Takada, Prog. Theor. Phys. Suppl. No. 141 (2001), 179[PTP].
- F. Sakata, T. Marumori, Y. Hashimoto, H. Tsukuma, Y. Yamamoto, J. Terasaki, Y. Iwasawa and H. Itabashi, Springer Proceedings in Physics, 58 (Springer-Verlag Berlin Heidelberg, 1991), p. 187.
- T. Yukawa and T. Ishikawa, Prog. Theor. Phys. Suppl. No. 98 (1989), 157[PTP].
- L. D. Landau and E. M. Lifshitz, Statistical Physics, pt. 1 (Butterworth-Heinemann, Oxford, 1980).
- W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C, 2nd ed. (CAMBRIDGE, 1992).
- Rubin. H. Landau and M. J. Paez, Computational Physics, Problem Solving With Computers (Wiley-Interscience, NY, 1997).
-
J. B. French, P. A. Mello and A. Pandey, Ann. of Phys. 113 (1978), 277[CrossRef].
-
A. Pandey, Ann. of Phys. 119 (1979), 170[CrossRef].
