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

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.

28 pages, 1 figure to appear in Annals of Physics

References in corpus (4)

• Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
• Variational Thomas-Fermi Theory of a Nonuniform Bose Condensate at Zero Temperature
• Non-ideal Boson system in the Gaussian approximation
• Gaussian Time-Dependent Variational Principle for Bosons Contact Interaction in one dimension

Cited by in corpus (5)

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• A Complex Chemical Potential: Signature of Decay in a Bose-Einstein Condensate
• BEC From a Time-Dependent Variational Point of View
• Generalized Random Phase Approximation and Gauge Theories