Monte Carlo calculation of the radial distribution function of quantum hard spheres at finite temperatures

The Green's function Monte Carlo method is generalized to treat quantum systems at non-zero temperature. The algorithm that is developed absolutely requires importance sampling to make it feasible. The nature of the importance sampling transformation needed for an efficient algorithm is discussed in theory and practice. As a demonstration of the principles, we carry out a calculation of the two body contribution to the radial distribution function and the second virial coefficient of a hard sphere fluid. Accurate numerical results are obtained. It is also shown how improvement in the structure of the importance function can lead to dramatic improvements in computational efficiency. A method is described, and successfully applied, whereby an importance function may be determined in large part during the Monte Carlo, rather than a priori. Finally, we conjecture that importance sampling can also be applied to the sums over permutations for treating boson or fermion systems.