Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2005-11-17
Prog. Theor. Phys., Vol.114, No.5 (November 2005)
Nonlinear Sciences
Chaotic Dynamics
13 pages, 4 figures
Scientific paper
10.1143/PTP.114.929
Extending the argument of Ref.\citen{[4]} to the long-range spectral statistics of classically integrable quantum systems, we examine the level number variance, spectral rigidity and two-level cluster function. These observables are obtained by applying the approach of Berry and Robnik\cite{[0]} and the mathematical framework of Pandey \cite{[2]} to systems with infinitely many components, and they are parameterized by a single function $\bar{c}$, where $\bar{c}=0$ corresponds to Poisson statistics, and $\bar{c}\not=0$ indicates deviations from Poisson statistics. This implies that even when the spectral components are statistically independent, non-Poissonian spectral statistics are possible.
Makino Hiroki
Tasaki Shuichi
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