Bogomolny E, Giraud O, Schmit C
Laboratoire de Physique Théorique et Modèles Statistiques, Université de Paris XI, Bâtiment 100, 91405 Orsay Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 2):056214. doi: 10.1103/PhysRevE.65.056214. Epub 2002 May 17.
The exact computation of the nearest-neighbor spacing distribution P(s) is performed for a rectangular billiard with a pointlike scatterer inside for periodic and Dirichlet boundary conditions, and it is demonstrated that when s-->infinity this function decreases exponentially. Together with the results of Bogomolny, Gerland, and Schmit [Phys. Rev. E 63, 036206 (2001)], it proves that spectral statistics of such systems is of intermediate type characterized by level repulsion at small distances and exponential fall-off of the nearest-neighbor distribution at large distances. The calculation of the nth nearest-neighbor spacing distribution P(n)(s) and its asymptotics is performed as well for any boundary conditions.
对于内部有一个点状散射体的矩形台球，在周期性边界条件和狄利克雷边界条件下，精确计算了最近邻间距分布(P(s))，并且证明了当(s\to\infty)时，该函数呈指数下降。结合博戈莫尔尼、格兰德和施密特的结果[《物理评论E》63, 036206 (2001)]，证明了此类系统的谱统计属于中间类型，其特征是在小距离处能级排斥，在大距离处最近邻分布呈指数衰减。对于任何边界条件，还计算了第(n)个最近邻间距分布(P^{(n)}(s))及其渐近行为。
