Energy estimators for random series path-integral methods

Abstract

We perform a thorough analysis on the choice of estimators for random series path integral methods. In particular, we show that both the thermodynamic (T-method) and the direct (H-method) energy estimators have finite variances and are straightforward to implement. It is demonstrated that the agreement between the T-method and the H-method estimators provides an important consistency check on the quality of the path integral simulations. We illustrate the behavior of the various estimators by computing the total, kinetic, and potential energies of a molecular hydrogen cluster using three different path integral techniques. Statistical tests are employed to validate the sampling strategy adopted as well as to measure the performance of the parallel random number generator utilized in the Monte Carlo simulation. Some issues raised by previous simulations of the hydrogen cluster are clarified.

15 pages, 1 figure, 3 tables

References in corpus (6)

• The Approach to Ergodicity in Monte Carlo Simulations
• Optimal series representations for numerical path integral simulations
• Optimal Energy Estimation in Path-Integral Monte Carlo Simulations
• Numerical implementation of some reweighted path integral methods
• Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation
• Asymptotic convergence of the partial averaging technique

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• Convergence Characteristics of the Cumulant Expansion for Fourier Path Integrals
• On the efficient Monte Carlo implementation of path integrals