  A numerically exact path integral treatment of the absorption and emission
spectra of open quantum systems is presented that requires only the
straightforward solution of a stochastic differential equation. The approach
converges rapidly enabling the calculation of spectra of large excitonic
systems across the complete range of system parameters and for arbitrary bath
spectral densities. With the numerically exact absorption and emission
operators one can also immediately compute energy transfer rates using the
multi-chromophoric Forster resonant energy transfer formalism. Benchmark
calculations on the emission spectra of two level systems are presented
demonstrating the efficacy of the stochastic approach. This is followed by
calculations of the energy transfer rates between two weakly coupled dimer
systems as a function of temperature and system-bath coupling strength. It is
shown that the recently developed hybrid cumulant expansion is the only
perturbative method capable of generating uniformly reliable energy transfer
rates and spectra across a broad range of system parameters.
