skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Low variance energy estimators for systems of quantum Drude oscillators: Treating harmonic path integrals with large separations of time scales

Abstract

In the effort to develop atomistic models capable of accurately describing nanoscale systems with complex interfaces, it has become clear that simple treatments with rigid charge distributions and dispersion coefficients selected to generate bulk properties are insufficient to predict important physical properties. The quantum Drude oscillator model, a system of one-electron pseudoatoms whose 'pseudoelectrons' are harmonically bound to their respective 'pseudonuclei', is capable of treating many-body polarization and dispersion interactions in molecular systems on an equal footing due to the ability of the pseudoatoms to mimic the long-range interactions that characterize real materials. Using imaginary time path integration, the Drude oscillator model can, in principle, be solved in computer operation counts that scale linearly with the number of atoms in the system. In practice, however, standard expressions for the energy and pressure, including the commonly used virial estimator, have extremely large variances that require untenably long simulation times to generate converged averages. In this paper, low-variance estimators for the internal energy are derived, in which the large zero-point energy of the oscillators does not contribute to the variance. The new estimators are applicable to any system of harmonic oscillators coupled to one another (or to the environment) via an arbitrarymore » set of anharmonic interactions. The variance of the new estimators is found to be much smaller than standard estimators in three example problems, a one-dimensional anharmonic oscillator and quantum Drude models of the xenon dimer and solid (fcc) xenon, respectively, yielding 2-3 orders of magnitude improvement in computational efficiency.« less

Authors:
;  [1]
  1. IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598 (United States)
Publication Date:
OSTI Identifier:
20991221
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 126; Journal Issue: 7; Other Information: DOI: 10.1063/1.2424708; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ANHARMONIC OSCILLATORS; ATOMS; CHARGE DISTRIBUTION; ELECTRONS; EQUATIONS OF STATE; HARMONIC OSCILLATORS; INTERACTION RANGE; NANOSTRUCTURES; OSCILLATORS; PATH INTEGRALS; PHYSICAL PROPERTIES; SIMULATION; XENON

Citation Formats

Whitfield, Troy W., and Martyna, Glenn J. Low variance energy estimators for systems of quantum Drude oscillators: Treating harmonic path integrals with large separations of time scales. United States: N. p., 2007. Web. doi:10.1063/1.2424708.
Whitfield, Troy W., & Martyna, Glenn J. Low variance energy estimators for systems of quantum Drude oscillators: Treating harmonic path integrals with large separations of time scales. United States. doi:10.1063/1.2424708.
Whitfield, Troy W., and Martyna, Glenn J. Wed . "Low variance energy estimators for systems of quantum Drude oscillators: Treating harmonic path integrals with large separations of time scales". United States. doi:10.1063/1.2424708.
@article{osti_20991221,
title = {Low variance energy estimators for systems of quantum Drude oscillators: Treating harmonic path integrals with large separations of time scales},
author = {Whitfield, Troy W. and Martyna, Glenn J.},
abstractNote = {In the effort to develop atomistic models capable of accurately describing nanoscale systems with complex interfaces, it has become clear that simple treatments with rigid charge distributions and dispersion coefficients selected to generate bulk properties are insufficient to predict important physical properties. The quantum Drude oscillator model, a system of one-electron pseudoatoms whose 'pseudoelectrons' are harmonically bound to their respective 'pseudonuclei', is capable of treating many-body polarization and dispersion interactions in molecular systems on an equal footing due to the ability of the pseudoatoms to mimic the long-range interactions that characterize real materials. Using imaginary time path integration, the Drude oscillator model can, in principle, be solved in computer operation counts that scale linearly with the number of atoms in the system. In practice, however, standard expressions for the energy and pressure, including the commonly used virial estimator, have extremely large variances that require untenably long simulation times to generate converged averages. In this paper, low-variance estimators for the internal energy are derived, in which the large zero-point energy of the oscillators does not contribute to the variance. The new estimators are applicable to any system of harmonic oscillators coupled to one another (or to the environment) via an arbitrary set of anharmonic interactions. The variance of the new estimators is found to be much smaller than standard estimators in three example problems, a one-dimensional anharmonic oscillator and quantum Drude models of the xenon dimer and solid (fcc) xenon, respectively, yielding 2-3 orders of magnitude improvement in computational efficiency.},
doi = {10.1063/1.2424708},
journal = {Journal of Chemical Physics},
number = 7,
volume = 126,
place = {United States},
year = {Wed Feb 21 00:00:00 EST 2007},
month = {Wed Feb 21 00:00:00 EST 2007}
}
  • We use an optimal estimator to study the variance of the WMAP 9 CMB field at low resolution, in both temperature and polarization. Employing realistic Monte Carlo simulation, we find statistically significant deviations from the ΛCDM model in several sky cuts for the temperature field. For the considered masks in this analysis, which cover at least the 54% of the sky, the WMAP 9 CMB sky and ΛCDM are incompatible at ≥ 99.94% C.L. at large angles ( > 5°). We find instead no anomaly in polarization. As a byproduct of our analysis, we present new, optimal estimates of themore » WMAP 9 CMB angular power spectra from the WMAP 9 year data at low resolution.« less
  • This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if themore » dynamic of the system is related to a set of ODEs.« less
  • We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest, these systems are analytically intractable, and one has to resort to computational methods to estimate stationary values of cost functions. In this work, we introduce a novel variance reduction algorithm for stochastic chemical kinetics, inspired by related methods in queueing theory, in particular the use of shadow functions. Using two numerical examples, we demonstrate the efficiency of the method for the calculation of steady-state parametric sensitivities and evaluate its performance in comparison to other estimation methods.