Blip decomposition of the path integral: Exponential acceleration of realtime calculations on quantum dissipative systems
The realtime path integral representation of the reduced density matrix for a discrete system in contact with a dissipative medium is 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, it is shown that 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. This exact decomposition reduces the number of terms by a factor that increases exponentially with propagation time. Further, under conditions (moderately high temperature and/or dissipation strength) that lead primarily to incoherent dynamics, the “fully incoherent limit” zeroblip term of the series provides a reasonable approximation to the dynamics, and the blip series converges rapidly to the exact result. Retention of only the blips required for satisfactory convergence leads to speedup of fullmemory path integral calculations by many orders of magnitude.
 Authors:

^{[1]}
 Departments of Chemistry and Physics, University of Illinois, Urbana, Illinois 61801 (United States)
 Publication Date:
 OSTI Identifier:
 22436544
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 13; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; DECOMPOSITION; DENSITY MATRIX; ITERATIVE METHODS; PATH INTEGRALS; WAVE FUNCTIONS