Properties of He-4 in one dimension

It has been suggested recently that He-4 can be prepared and studied as a q uasi one-dimensional quantum fluid. We calculate the static and dynamic pro perties of one-dimensional He-4 using variational methods based upon the Ja strow-Feenberg wavefunction and its extension to dynamic systems with time- dependent, correlated wavefunctions. He-4 is just barely self-bound with a binding energy The zero temperature equation of state shows that in one-dim ension of 0.002 K at a density of 0.036 Angstrom(-1). We also calculate the excitation spectrum including corrections that contain multi-phonon proces ses and study the density dependence of the roton feature as well as the st atic response function. In addition we demonstrate the presence of strong a nomalous dispersion in the phonon regime. Finally, we introduce a He-3 impu rity and calculate the zero concentration chemical potential as a function of He-4 linear density. We also compute the He-3-He-3 effective interaction in the He-4 background and compute the energy of dimerization.