  We discuss a modification to Random Matrix Theory eigenstate statistics, that
systematically takes into account the non-universal short-time behavior of
chaotic systems. The method avoids diagonalization of the Hamiltonian, instead
requiring only a knowledge of short-time dynamics for a chaotic system or
ensemble of similar systems. Standard Random Matrix Theory and semiclassical
predictions are recovered in the limits of zero Ehrenfest time and infinite
Heisenberg time, respectively. As examples, we discuss wave function
autocorrelations and cross-correlations, and show that significant improvement
in accuracy is obtained for simple chaotic systems where comparison can be made
with brute-force diagonalization. The accuracy of the method persists even when
the short-time dynamics of the system or ensemble is known only in a classical
approximation. Further improvement in the rate of convergence is obtained when
the method is combined with the correlation function bootstrapping approach
introduced previously.
