We derive the real-space path integral formulations of Widom’s test particle method and grand canonical Monte Carlo (GCMC). We apply these simulation methods to hydrogen and neon at temperatures ranging from 30 to 120 K. In addition, in order to explore configuration space both efficiently and ergodically, our implementation involves multiple time step hybrid Monte Carlo. Agreement between experiment and simulation for chemical potentials (Widom) and densities (GCMC) is very good over the entire temperature range, even when quantum effects are large.
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Wang et al. (1997) studied this question.