An optimized random phase approximation for the dynamics of tunneling systems in condensed phases

We derive an optimized random phase approximation from an expansion of the free energy in terms of the generating functional. We apply the theory to a quantum mechanical tunneling system coupled to a Gaussian bath. The theory reproduces both short-time behavior and long-time averages of (real time) correlation functions, and compares favorably with both nonoptimized RPA and the cumulant expansion.