title: Spectral statistics of permutation matrices.
abstract: 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.
authors.affiliation: Department of Physics of Complex Systems, Weizmann Institute of Science, , Rehovot 76100, Israel.
authors.forename: Idan
authors.initials: I
authors.lastname: Oren
authors.forename: Uzy
authors.initials: U
authors.lastname: Smilansky
keywords: permutation matrices; random matrix theory; spectral statistics