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

For three model systems: hard rods, the Morse potential and the Lennard-Jon es 6-12 potential, we calculate equations of state and the low-lying excita tions using non-perturbative variational theory. We examine the effect of d imerization 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, He-4 at absolute zero is just barely self-bound with a bind ing energy of 0.002 K at a density of 0.036 Angstrom(-1). We calculate the Feynman excitation spectrum and we demonstrate the presence of strong anoma lous dispersion in the phonon regime. Finally, we introduce He-3 impurities and calculate the zero concentration chemical potential, the He-3-He-3 eff ective interaction in the 4He background and the energy of dimerization. (C ) 2000 Elsevier Science B.V. All rights reserved.