Displaced path integral formulation for the momentum distribution of quantum particles

TL;DR

This paper introduces a novel displaced path integral method to efficiently compute the proton momentum distribution in hydrogen-bonded systems, enhancing interpretability and computational efficiency.

Contribution

A new estimator for the end-to-end distribution of Feynman paths that factorizes free particle and environmental effects, with applications to water models and ice.

Findings

Factorization of free particle and environmental contributions

Enhanced computational efficiency in momentum distribution calculations

Application to empirical water models and ab-initio ice

Abstract

The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end to end distribution of the Feynman paths, i.e. the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab-initio ice, and one dimensional model systems.