COMMENT: Comment on energy level statistics in the mixed regime
COMMENT: Comment on energy level statistics in the mixed regime
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评论：对混合制度下能源水平统计的评论
DOI：
10.1088/0305-4470/30/24/037
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
T. Prosen
中科院分区：
文献类型：
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作者：
M. Robnik;T. Prosen
我们评论了 Abul-Magd (1996 29 1) 最近关于混合状态下的能级统计的论文，即具有混合经典动力学，其中规则区域和混沌区域在相空间中共存。我们指出，他对能级排斥函数 r(S)（条件概率密度）的加性性质的基本假设，即与经典分数相空间体积成比例地将其线性划分为规则部分和混沌部分，并且是不合理的，因为除其他外，它依赖于贝里遍历假设的类型，然而，该假设仅在遍历系统的齐次系综中是正确的，而不是在可积系统的邻域中。因此，他所得到的分布不能被视为理论上有充分根据的对象。我们指出半经典极限能级间距分布必须是 Berry - Robnik (1984) 类型，并解释我们在近半经典状态下观察到的布罗迪型（具有分数幂律能级排斥）的过渡行为，其中有效值还不够小。因此，我们参考之前的论文（Prosen and Robnik 1994 26 8059）中的推导、论证和结论，并再次解释这个双过渡区域的行为。
We comment on the recent paper by Abul-Magd (1996 29 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 and is not justified, since among other things, it relies on the type of Berry's ergodic assumption, which, however, is only correct in a homogeneous ensemble of ergodic systems, 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 is not yet small enough. Thus we refer to the derivation, arguments and conclusions in our previous paper (Prosen and Robnik 1994 26 8059), and explain again the behaviour in this double transition region.