Phase space path integrals in Monte Carlo quantum dynamics

In this article we present two phase space path integrals in terms of coherent states. The first one is derived in a standard fashion but using a nonstandard resolution of the identity in terms of coherent states with different width parameters. The second path integral emerges from a novel phase space representation in terms of coherent states distributed on n-dimensional manifolds embedded in the 2n-dimensional phase space of an n-degree-of-freedom system. These states are shown to form locally complete basis sets since we show that fairly smooth and localized functions can be expanded in terms of them in a unique way. In this representation the time evolution operator can be cast in the form of a phase space path integral. Both path integrals can be evaluated by straightforward implementation of Monte Carlo methods. In both cases the probability amplitude between two phase points turns out to be proportional to the average of the phase, e(i/hl integral(p dq-H dt))(P d4-H dr), over a Markov process of phase space paths consisting of classical trajectories interrupted at intervals by Gaussian ''quantum jumps.'' The numerical evaluation of these expressions through importance sampling is demonstrated. (C) 1996 American Institute of Physics.