Recent progress in numerical methods for evaluating the real-time path integral in
dissipative harmonic environments is reviewed. Quasi-adiabatic propagators constructed
numerically allow convergence of the path integral with large time increments. Integration of
the harmonic bath leads to path integral expressions that incorporate the exact dynamics of
the quantum particle along the adiabatic path, with an influence functional that describes
nonadiabatic corrections. The resulting quasi-adiabatic propagator path integral is …