Tensor propagator with weight-selected paths for quantum dissipative dynamics with long-memory kernels

The tensor multiplication scheme, which allows iterative evaluation of the path integral for quantum dissipative dynamics, is extended to processes involving long-memory kernels such as those occurring in low-frequency solvents. Rather than propagating the augmented reduced density tensor in full-dimensional space, we propose here including in the propagator tensor only those path segments which enter the path integral with appreciable weight. The appropriate path segments are selected according to their weights by importance sampling. Elimination of the vast majority of paths which make negligible contribution in the path integral results in dramatic reduction of the required storage.