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Diagonal approximation of the form factor of the unitary group

G. Berkolaiko
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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.

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G. Berkolaiko. 2005-09-21. Diagonal approximation of the form factor of the unitary group. https://doi.org/10.1088/0305-4470%2F39%2F4%2Fl01

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