skip to main content

SciTech ConnectSciTech Connect

Title: Blip decomposition of the path integral: Exponential acceleration of real-time calculations on quantum dissipative systems

The real-time 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” zero-blip 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 full-memory path integral calculations by many orders of magnitude.
Authors:
 [1]
  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