Forward-backward semiclassical dynamics with single-bead coherent state density

This paper reports investigations into the convergence properties of time correlation functions within the forward-backward semiclassical dynamics (FBSD) approximation when the Boltzmann phase space density function is not discretized by a sufficient number of path integral beads. Based on the behaviour of simple models and the relation to the more classical Kubo form, it is argued that the imaginary part of the correlation function generally converges faster than the real part and can be used to infer the latter via the detailed balance relation. Procedures are proposed for calculating Kubo-transformed correlation functions within the FBSD approximation. Numerical examples for model anharmonic systems (in one dimension or in contact with a dissipative bath) and Lennard-Jones fluids illustrate these ideas.