  The role of quantum coherence loss in mixed quantum-classical dynamical
systems is explored in the context of the theory of quantum decoherence
introduced recently by Bittner and Rossky. (J. Chem. Phys. {\bf 103}, 8130
(1995)). This theory, which is based upon the consistent histories
interpretation of quantum mechanics, introduces decoherence in the quantum
subsystem by carefully considering the relevant time and length scales over
which one must consider the effects of phase interference between alternative
histories of the classical subsystem. Such alternative histories are an
integral part of any quantum-classical computational scheme which employ
transitions between discrete quantum states; consequently, the coherences
between alternative histories have a profound effect on the transition
probability between quantum states. In this paper, we review the Bittner-Rossky
theory and detail a computational algorithm suitable for large-scale quantum
molecular dynamics simulations which implements this theory. Application of the
algorithm towards the relaxation of a photoexcited aqueous electron compare
well to previous estimates of the excited state survival time as well as to the
experimental measurements.
