Properties of many-boson systems in one dimension with application to ⁴He

For three model systems: hard rods, the Morse potential and the Lennard-Jones 6-12 potential, we calculate equations of state and the low-lying excitations using non-perturbative variational theory. We examine the effect of dimerization on the many-body equation of state and argue that dimerization is manifested as the appearance of a many-body bound state. We show that in one dimension, ⁴He at absolute zero is just barely self-bound with a binding energy of 0.002 K at a density of 0.036 Å^-1. We calculate the Feynman excitation spectrum and we demonstrate the presence of strong anomalous dispersion in the phonon regime. Finally, we introduce ³He impurities and calculate the zero concentration chemical potential, the ³He-³He effective interaction in the ⁴He background and the energy of dimerization.