Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comment on Energy Level Statistics in the Mixed Regime   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.

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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc