Properties of ⁴He in one dimension

It has been suggested recently that ⁴He can be prepared and studied as a quasi one-dimensional quantum fluid. We calculate the static and dynamic properties of one-dimensional ⁴He using variational methods based upon the Jastrow-Feenberg wavefunction and its extension to dynamic systems with time-dependent, correlated wavefunctions. The zero temperature equation of state shows that in one-dimension ⁴He is just barely self-bound with a binding energy of 0.002 K at a density of 0.036 angstrom^-1. We also calculate the excitation spectrum including corrections that contain multi-phonon processes and study the density dependence of the roton feature as well as the static response function. In addition we demonstrate the presence of strong anomalous dispersion in the phonon regime. Finally, we introduce a ³He impurity and calculate the zero concentration chemical potential as a function of ⁴He linear density. We also compute the ³He-³He effective interaction in the ⁴He background and compute the energy of dimerization.