G Berkolaiko 2006 J. Phys. A: Math. Gen. 39 L77 doi:10.1088/0305-4470/39/4/L01
Diagonal approximation of the form factor of the unitary group
FREE ARTICLEG Berkolaiko
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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].
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Issue 4 (27 January 2006)
Received 21 September 2005, in final form 15 November 2005
Published 11 January 2006
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Diagonal approximation of the form factor of the unitary group
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