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Starting from a semiclassical approach recently developed for spectralcorrelation functions of quantum systems whose classical dynamics is chaotic,we focus on the case of broken time-reversal symmetry, the so-called unitaryclass. We obtain to all orders in perturbation theory the non-oscillatory partsof all correlation functions, showing that the off-diagonal contributions tothese correlation functions cancel and the conjectured universailty holds. Theinnovation that allows this calculation to be performed is the introduction ofan auxiliary matrix model which is governed by the same diagrammatic rules asthe semiclassical approach and which can be exactly solved.

Full perturbative calculation of spectral correlation functions for chaotic systems in the unitary symmetry class