Monte Carlo evaluation of real-time Feynman path integrals for quantal many-body dynamics: Distributed approximating functions and Gaussian sampling

Donald J. Kouri, Wei Zhu, Xin Ma, Bernard Pettitt, David K. Hoffman

Research output: Contribution to journalArticle

61 Citations (Scopus)

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)2σ2(0)/(2σ4(0) + ℏ2τ2/m2)], 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 languageEnglish (US)
Pages (from-to)9622-9630
Number of pages9
JournalJournal of Physical Chemistry
Volume96
Issue number24
StatePublished - 1992
Externally publishedYes

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sampling
Sampling
evaluation
propagation
Morse potential
Importance sampling
Monte Carlo methods
Polynomials
Monte Carlo method
polynomials
envelopes
occurrences
products
configurations

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

Monte Carlo evaluation of real-time Feynman path integrals for quantal many-body dynamics : Distributed approximating functions and Gaussian sampling. / Kouri, Donald J.; Zhu, Wei; Ma, Xin; Pettitt, Bernard; Hoffman, David K.

In: Journal of Physical Chemistry, Vol. 96, No. 24, 1992, p. 9622-9630.

Research output: Contribution to journalArticle

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