Diagonal approximation of the form factor of the unitary group
arXiv:nlin/0509037 · doi:10.1088/0305-4470/39/4/L01
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 to infinity, the diagonal approximation becomes ``exact'', that is converges to the full form factor.
9 pages