GAUSSIAN TIME-DEPENDENT VARIATIONAL PRINCIPLE FOR BOSONS .1. UNIFORM CASE

We investigate the Dirac time-dependent variational method for a syste m of non-ideal Bosons interacting through an arbitrary two body potent ial. The method produces a set of non-linear time dependent equations for the variational parameters. In particular we have considered small oscillations about equilibrium. We obtain generalized RPA equations t hat can be understood as interacting quasi-bosons, usually mentioned i n the literature as having a gap. The result of this interaction provi des us with scattering properties of these quasi-bosons including poss ible bound-states, which can include zero modes. In fact the zero mode bound state can be interpreted as a new quasi-boson with a gapless di spersion relation. Utilizing these results we discuss a straightforwar d scheme for introducing temperature. (C) 1997 Academic Press.