  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.
