The Blip Decomposition

Recent work has shown that the real-time path integral representation of the reduced density matrix for a discrete system in contact with a dissipative medium can be rewritten in terms of the number of blips, i.e., elementary time intervals over which the forward and backward paths are not identical. For a given set of blips, the path sum with respect to the coordinates of all remaining time points is isomorphic to that for the wavefunction of a system subject to an external driving term, and thus can be summed by an inexpensive iterative procedure. The gain from this exact decomposition increases exponentially with propagation time. Further, under conditions (moderately high temperature and/or dissipation strength) that lead primarily to incoherent dynamics, the blip series converges rapidly to the exact result.  Retention of only the blips required for satisfactory convergence leads to speedup of full-memory path integral calculations by many orders of magnitude.


An iterative decomposition of the blip-summed path integral has been developed, which allows propagation to long times, offering dramatic computational savings in regimes characterized incoherent dynamics.

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