Gaussian Time-Dependent Variational Principle for Bosons I - Uniform Case

TL;DR

This paper develops a time-dependent variational approach for non-ideal bosonic systems, deriving generalized RPA equations that describe interacting quasi-bosons, including bound states and zero modes, with implications for finite temperature analysis.

Contribution

It introduces a novel variational method for bosons that yields generalized RPA equations with detailed scattering and bound-state properties, including zero modes.

Findings

Derived non-linear time-dependent equations for bosonic systems.

Identified bound states and zero modes in the quasi-boson spectrum.

Proposed a scheme to incorporate temperature effects.

Abstract

We investigate the Dirac time-dependent variational method for a system of non-ideal Bosons interacting through an arbitrary two body potential. 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 that can be understood as interacting quasi-bosons, usually mentioned in the literature as having a gap. The result of this interaction provides us with scattering properties of these quasi-bosons including possible 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 dispersion relation. Utilizing these results we discuss a straightforward scheme for introducing temperature.