Path Integral Monte Carlo calculation of momentum distribution in solid \^4\He

TL;DR

This study uses path integral Monte Carlo methods to analyze the momentum distribution in solid helium-4, revealing temperature independence in perfect crystals and unique features in crystals with vacancies, especially at low temperatures.

Contribution

It introduces a detailed quantum Monte Carlo analysis of momentum distribution in solid He, highlighting effects of vacancies and temperature on quantum behavior.

Findings

n(k) is temperature-independent in perfect crystals

n(k) differs from classical Maxwell-Boltzmann distribution

Vacancies induce a peak in n(k) at low temperatures

Abstract

We perform calculations of the momentum distribution n(k) in solid \^4\He by means of path integral Monte Carlo methods. We see that, in perfect crystal, n(k) does not depend on temperature T and that is different from the classical Gaussian shape of Maxwell-Boltzmann distribution, even though these discrepancies decrease when the density of the system increases. In crystal presenting vacancies, we see that for T \ge 0.75K, n(k) presents the same behavior as in the perfect crystal, but, at lower T, it presents a peak when k\to0.