Excitations of Liquid 4 He in Disorder

The dynamic structure factor S(q, w) for a model of superfluid 4He in disorder is evaluated using Path Integral Monte Carlo and Maximum Entropy methods. Disorder is represented by randomly distributed static impurities interacting with the 4He atoms via a simple attractive potential. The potential is parametrized to yield different values of the variance and correlation length of the resulting disordering environment. New weight in S(q, w) at low w (i.e., low energy excitations) is induced by disorder, as predicted in some previous calculations, and S(q, w) is broadened. Assuming that S(q, w) in disorder is dominated by a single peak, just as in the pure superfluid, the data suggest that the peak position is shifted by the disorder from the bulk value with a unique q dependence. The static structure factor S(q) is reduced at all wave vectors with increased impurity concentration.