Abstract. The form factor of the unitary group U(N) endowed with the Haar measure characterizes the correlations within the spectrum of a typical unitary matrix. It can be decomposed into a sum over pairs of 'periodic orbits', where by periodic orbit we understand any sequence of matrix indices. From here the diagonal approximation can be defined in the usual fashion as a sum only over pairs of identical orbits. We prove that as we take the dimension N to infinity, the diagonal approximation becomes 'exact', that is converges to the full form factor in the interval τ [0, 1].

PACS numbers: 05.45.Mt, 02.10.De, 02.50.Ga, 05.10.Gg, 02.70.Hm

Print publication: Issue 4 (27 January 2006)
Received 21 September 2005, in final form 15 November 2005
Published 11 January 2006