补遗：亏格为零的可积量子映射的能级间隔
Addendum: Level Spacings for Integrable Quantum Maps in Genus Zero
摘要：
在本附录中，我们在多项式相位的情况下加强了math-ph/0002010的结果。证明了2-球面上某些可积量子映射的关联函数对的Cesaro平均在N层上几乎总是趋于Poisson（一致极限）.量子映射是哈密顿量的指数，其形式为a p（I）+ b I，其中I是作用量，其中p是多项式，a，b是两个实数。我们证明了对于任何这样的家庭和几乎所有的a，b，对相关趋于泊松平均在N。结果涉及指数和的Weyl估计和连分式的新度量结果。他们的动机是比较的结果math-ph/0002010与一些独立的结果对相关的分数部分的多项式Rudnick-Sarnak。
英文摘要：
In this addendum we strengthen the results of math-ph/0002010 in the case of polynomial phases. We prove that Cesaro means of the pair correlation functions of certain integrable quantum maps on the 2-sphere at level N tend almost always to the Poisson (uniform limit). The quantum maps are exponentials of Hamiltonians which have the form a p(I) + b I, where I is the action, where p is a polynomial and where a,b are two real numbers. We prove that for any such family and for almost all a,b, the pair correlation tends to Poisson on average in N. The results involve Weyl estimates on exponential sums and new metric results on continued fractions. They were motivated by a comparison of the results of math-ph/0002010 with some independent results on pair correlation of fractional parts of polynomials by Rudnick-Sarnak.
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