Real time path integral methods for a system coupled to an anharmonic bath

We propose an efficient path integral scheme for calculating the quantum dynamics of an arbitrary one-dimensional system coupled nonlinearly to many anharmonic noninteracting "bath" degrees of freedom. The starting point is an improved discretization of the path integral in terms of numerically constructed propagators [Chem. Phys. Lett. 193, 435 (1992)]. The resulting influence functional is comprised of one-dimensional correlation functions with step-structured time-dependent potentials and therefore is similar in structure to that employed in the spin-boson calculations of Coalson [J. Chem. Phys. 86, 995 (1987)]. In the present case, though, the influence functional is nonlinear and is computed using numerical iterative wave function propagation methods. Numerical tests on a system coupled to ten anharmonic oscillators demonstrate the efficiency of the proposed scheme, which requires numerical effort that scales only linearly with the number of anharmonic bath degrees of freedom.