It has been suggested recently that ${}^4\mathrm{He}$ can be prepared and studied as a quasi-one-dimensional quantum fluid. In this paper we calculate the static and dynamic properties of one-dimensional ${}^4\mathrm{He}$ using variational methods based upon the Jastrow-Feenberg wave function and its extension to dynamic systems with time-dependent, correlated wave functions. We calculate the zero temperature equation of state and show that in one dimension ${}^4\mathrm{He}$ is just barely self-bound with a binding energy of 0.002 K at a density of 0.036 ${\mathrm{\AA }}^{-1}.$ We calculate the Feynman excitation spectrum and corrections that contain multiphonon 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 ${}^3\mathrm{He}$ impurity and calculate the zero concentration chemical potential as a function of ${}^4\mathrm{He}$ linear density. We also compute the ${}^3\mathrm{He}$-${}^3\mathrm{He}$ effective interaction in the ${}^4\mathrm{He}$ background and compute the energy of dimerization.

• Received 30 March 1999

DOI:https://doi.org/10.1103/PhysRevB.60.13038