Roton wave-packets in 3-dimensional and 2-dimensional He-4

We have obtained new information on the elementary excitations in superfluid He-4 by studying local observables relative to roton wave-packets built from accurate variational representations of the excited states. The same technique has been applied also to study a pure 2-Dimensional system, where the spectrum, computed through a variational Monte Carlo simulation, still shows a modified phonon-maxon-roton dispersion relation. In the roton region, collective quantum effects are present, but when the average momentum of the wave-packet matches with the wave-vector of the roton minimum the interference effects between neighboring atoms disappear and the local density and momentum essentially coincide with those of a single particle excitation. A roton, as well as a single particle excitation, has a velocity vector field which is very similar to that of a smoke-ring scaled down to atomic size.