Path integral Monte Carlo simulations of silicates
  We investigate the thermal expansion of crystalline SiO$_2$ in the $\beta$-- cristobalite and the $\beta$-quartz structure with path integral Monte Carlo (PIMC) techniques. This simulation method allows to treat low-temperature quantum effects properly. At temperatures below the Debye temperature, thermal properties obtained with PIMC agree better with experimental results than those obtained with classical Monte Carlo methods. 
Chr. Rickwardt, P. Nielaba, M. H. M\"user, K. Binder