Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1997-06-23
Nonlinear Sciences
Chaotic Dynamics
11 pages in LaTeX; two figures available upon request
Scientific paper
10.1088/0305-4470/30/24/037
We comment on the recent paper by Abul-Magd (J.Phys.A: Math.Gen. 29 (1996) 1) concerning the energy level statistics in the mixed regime, i.e. such having the mixed classical dynamics where regular and chaotic regions coexist in the phase space. We point out that his basic assumption on the additive property of the level-repulsion function $r(S)$ (conditional probability density) in the sense of dividing it linearly into the regular and chaotic part in proportion to the classical fractional phase space volumes $\rho_1$ and $\rho_2=q$ is not justified, since among other things, it relies on the type of Berry's ergodic assumption, which however is right only in a homogeneous ensemble of ergodic systems, but not in the neighbourhood of an integrable system. Thus his resulting distribution cannot be regarded as a theoretically well founded object. We point out that the semiclassical limiting energy level spacing distribution must be of Berry-Robnik (1984) type, and explain what transitional behaviour of the Brody-type (with fractional power-law energy level repulsion) we observe in the near semiclassical regime where effective $\hbar$ is not yet small enough. Thus we refer to the derivation, arguments and conclusions in our paper (Prosen and Robnik, J.Phys.A: Math.Gen. 26 (1994) 8059), and explain again the behaviour in this double transition region.
Prosen Tomaz
Robnik Marko
No associations
LandOfFree
Comment on Energy Level Statistics in the Mixed Regime does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Comment on Energy Level Statistics in the Mixed Regime, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Comment on Energy Level Statistics in the Mixed Regime will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-337361