Department of Physics of Complex Systems, Weizmann Institute of Science, , Rehovot 76100, Israel.
Philos Trans A Math Phys Eng Sci. 2013 Dec 16;372(2007):20120508. doi: 10.1098/rsta.2012.0508. Print 2014 Jan 28.
We compute the mean two-point spectral form factor and the spectral number variance for permutation matrices of large order. The two-point correlation function is expressed in terms of generalized divisor functions, which are frequently discussed in number theory. Using classical results from number theory and casting them in a convenient form, we derive expressions which include the leading and next to leading terms in the asymptotic expansion, thus providing a new point of view on the subject, and improving some known results.
我们计算了大阶置换矩阵的平均两点谱形函数和谱数方差。两点相关函数用广义除数函数表示，这些函数在数论中经常被讨论。我们利用数论中的经典结果，并将其转化为方便的形式，推导出了包括渐近展开的主导项和次主导项的表达式，从而为该主题提供了一个新的视角，并改进了一些已知的结果。
