  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 how the approach leads to a
significant improvement in accuracy for simple chaotic systems where comparison
can be made with brute-force diagonalization.
