The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the spectral fluctuatations of these systems is available only up to this order. For a complete understanding of spectral properties it is highly desirable to study the higher order spectral correlations. This will also inform us about the limitations of random matrix theory in modelling the properties of quantum chaotic systems. Our main purpose in this paper is to carry out this study by a semiclassical calculation for the quantum maps; however results are also valid for time-independent systems
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