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Spectral statistics of permutation matrices
1Department of Physics of Complex Systems, Weizmann Institute of Science, , Rehovot 76100, Israel.
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.
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