TITLE

Analysis of the statistical errors in conditioned real time path integral methods

AUTHOR(S)
Amini, Abolfazl M.; Herman, Michael F.
PUB. DATE
October 1993
SOURCE
Journal of Chemical Physics;10/1/1993, Vol. 99 Issue 7, p5087
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
An analysis is provided of the statistical errors in the Monte Carlo evaluation of the conditioned real time discretized path integral propagator. The analysis considers the case of a harmonic potential. For this case, all the required integrals can be performed analytically. This analysis is also relevant to a semiclassical evaluation of the integrals in more general problems. It is found (in the simplest case) that the optimal relative statistical error per independent sampling is proportional to DD/2, where D is the dimensionality of the integrand. Therefore, the number of Monte Carlo samplings must scale as DD in order to achieve a desired level of accuracy. Since D is proportional to the number of time steps in the discretized path integral, this analysis demonstrates that the length of the calculations required increases very rapidly as the number of time steps is increased.
ACCESSION #
7648645

 

Related Articles

  • Reversible work based quantum transition state theory. Schenter, Gregory K.; Mills, Gregory; Jónsson, Hannes // Journal of Chemical Physics;11/15/1994, Vol. 101 Issue 10, p8964 

    A theoretical basis is presented for reversible work evaluation of transition rates within the framework of transition state theory. The method involves computing statistical averages of forces without having to evaluate transition state partition functions or densities, and therefore eliminates...

  • Path integral Monte Carlo study of the hydrated electron. Wallqvist, A.; Thirumalai, D.; Berne, B. J. // Journal of Chemical Physics;6/1/1987, Vol. 86 Issue 11, p6404 

    The structure of an excess electron in water at room temperature is investigated using the Feynman path integral technique. The interaction potential between the electron and water is modeled by an effective potential, made up of three terms: a static potential, a repulsive potential, and a...

  • Local parabolic reference approximation of thermal Feynman path integrals in quantum Monte Carlo... Chao, Cecilia E.; Andersen, Hans C. // Journal of Chemical Physics;12/15/1997, Vol. 107 Issue 23, p10121 

    Analyzes a local parabolic reference (LPR) propagator used in the numerical evaluation of discretized Feynman path integrals by Monte Carlo simulations. Form of the propagator; Approximations in the low temperature regime; Accuracy of the Monte Carlo path integrals; Calculation of the...

  • Computing conditional Wiener integrals of functionals of a general form. Dumas, W. M.; Tretyakov, M. V. // IMA Journal of Numerical Analysis;Jul2011, Vol. 31 Issue 3, p1217 

    A numerical method of second order of accuracy for computing conditional Wiener integrals of smooth functionals of a general form is proposed. The method is based on the simulation of a Brownian bridge via the corresponding stochastic differential equations (SDEs) and on ideas of the weak-sense...

  • Including quantum subsystem character within classical equilibrium simulations. Gomez, Maria A.; Peart, Patricia // Journal of Chemical Physics;7/21/2006, Vol. 125 Issue 3, p034105 

    A mixed quantum/classical density matrix approximation is derived. The density matrix makes use of quantum subsystem vibrational wave functions. The diagonal of the density matrix can be used as an equilibrium distribution in Monte Carlo simulations. The approximate distribution compares well...

  • A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies. Mielke, Steven L.; Truhlar, Donald G. // Journal of Chemical Physics;2016, Vol. 144 Issue 3, p1 

    Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing...

  • Molecular dynamics with quantum statistics: time correlation functions and weakly bound nano-clusters. Roy, Pierre-Nicholas // Theoretical Chemistry Accounts: Theory, Computation, & Modeling;Aug2006, Vol. 116 Issue 1-3, p274 

    An account of recent developments in the study of molecular dynamics with the inclusion of quantum exchange effects is presented. Approaches for quantum dynamical calculations are reviewed and the determination of time correlation functions is a special point of focus. It is shown that the exact...

  • Conformational properties of a polymer chain confined between two plates. Ishinabe, Takao // Journal of Chemical Physics;7/1/1985, Vol. 83 Issue 1, p423 

    The behavior of a polymer chain confined between parallel plates a distance D apart is studied by Monte Carlo calculations of self-avoiding walks for up to 100 steps on the tetrahedral lattice. Scaling predictions of Daoud and de Gennes are tested using the data obtained; they are consistent...

  • Monte Carlo simulation and phase behavior of nonadditive hard-core mixtures in two dimensions. Saija, F.; Giaquinta, P. V. // Journal of Chemical Physics;9/22/2002, Vol. 117 Issue 12, p5780 

    We report Monte Carlo results for the thermodynamic and structural properties of a mixture of equally sized hard discs that are characterized by a nonadditive collision diameter for particles belonging to unlike species. We calculated the phase-coexistence lines relative to fluid-fluid demixing...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics