1,283 research outputs found
Non-Poissonian level spacing statistics of classically integrable quantum systems based on the Berry-Robnik approach
Along the line of thoughts of Berry and Robnik\cite{[1]}, we investigated the
gap distribution function of systems with infinitely many independent
components, and discussed the level-spacing distribution of classically
integrable quantum systems. The level spacing distribution is classified into
three cases: Case 1: Poissonian if , Case 2: Poissonian
for large , but possibly not for small if , and
Case 3: sub-Poissonian if . Thus, even when the energy
levels of individual components are statistically independent, non-Poisson
level spacing distributions are possible.Comment: 5 pages, 0 figur
Long-Range Spectral Statistics of Classically Integrable Systems --Investigation along the Line of the Berry-Robnik Approach--
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 ,
where corresponds to Poisson statistics, and
indicates deviations from Poisson statistics. This implies that even when the
spectral components are statistically independent, non-Poissonian spectral
statistics are possible.Comment: 13 pages, 4 figure
Hierarchy of Chaotic Maps with an Invariant Measure
We give hierarchy of one-parameter family F(a,x) of maps of the interval
[0,1] with an invariant measure. Using the measure, we calculate
Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of
these maps analytically, where the results thus obtained have been approved
with numerical simulation. In contrary to the usual one-parameter family of
maps such as logistic and tent maps, these maps do not possess period doubling
or period-n-tupling cascade bifurcation to chaos, but they have single fixed
point attractor at certain parameter values, where they bifurcate directly to
chaos without having period-n-tupling scenario exactly at these values of
parameter whose Lyapunov characteristic exponent begins to be positive.Comment: 18 pages (Latex), 7 figure
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