A partial averaging strategy for low temperature Fourier path integral Monte Carlo calculations

Abstract

Partial averaging is a powerful technique for enhancing the convergence of Fourier path integral Monte Carlo with respect to the number of Fourier coefficients included in the calculation. In the original partial averaging method, a Fourier sine series expansion of the Feynman paths was implemented and higher-order Fourier modes were averaged over by virtue of a free particle reference system. In the present paper, it is shown that by making the alternative choice of a full Fourier series expansion of the paths and a locally harmonic reference system, the partial averaging technique can be improved for low temperature applications. This improvement is accomplished because the higher-order Fourier modes that partially average the potential are allowed to have locally harmonic fluctuations about the Feynman path centroid variable. The added statistical benefit from using path vs point estimators in the partial averaging scheme is also illustrated. Representative calculations are presented for a Morse oscillator at low temperature.