### Abstract

In this paper we report the initial steps in the development of a Monte Carlo method for evaluation of real-time Feynman path integrals for many-particle dynamics. The approach leads to Gaussian importance sampling for real-time dynamics in which the sampling function is short ranged due to the occurrence of Gaussian factors. These Gaussian factors result from the use of a generalization of our new discrete distributed approximating functions (DDAFs) to continuous distributed approximating functions (CDAFs) so as to replace the exact coordinate representation free-particle propagator by a "CDAF-class, free-particle propagator" which is highly banded. The envelope of the CDAF-class free propagator is the product of a "bare Gaussian", exp[-(x′ - x)^{2}σ^{2}(0)/(2σ^{4}(0) + ℏ^{2}τ^{2}/m^{2})], with a "shape polynomial" in (x′ - x)^{2}, where σ(0) is a width parameter at zero time (associated with the description of the wavepacket in terms of Hermite functions), τ is the time step (τ = t/N, where t is the total propagation time), and x and x′ are any two configurations of the system. The bare Gaussians are used for Monte Carlo integration of a path integral for the survival probability of a Gaussian wavepacket in a Morse potential. The approach appears promising for real-time quantum Monte Carlo studies based on the time-dependent Schrödinger equation, the time-dependent von Neumann equation, and related equations.

Original language | English (US) |
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Pages (from-to) | 9622-9630 |

Number of pages | 9 |

Journal | Journal of physical chemistry |

Volume | 96 |

Issue number | 24 |

DOIs | |

State | Published - Jan 1 1992 |

Externally published | Yes |

### ASJC Scopus subject areas

- Engineering(all)
- Physical and Theoretical Chemistry

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## Cite this

*Journal of physical chemistry*,

*96*(24), 9622-9630. https://doi.org/10.1021/j100203a013