Roton wave–packets in 3–Dimensional and 2–Dimensional 4He

We have obtained new information on the elementary excitations in superfluid ⁴ He 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.