Extended coupled-cluster method. III. Zero-temperature hydrodynamics of a condensed Bose fluid.

Abstract

The extended coupled-cluster method (ECCM) of quantum many-body theory, which has been studied and developed in earlier papers in this series, is now applied to condensed Bose systems. The formalism is seen to provide a concise and convenient description of quite general nonstatic states of such systems with arbitrary spatial inhomogeneity. The entire ECCM description is based on the equations of motion for the set of linked-cluster amplitudes which, we have shown, completely characterize an arbitrary quantum system with a Schr\"odinger dynamics. Since all such amplitudes obey the cluster property, and hence may be regarded as a set of quasilocal, many-body, classical order parameters, the formalism is in principle perfectly capable of describing phase transitions and states of topological excitation or deformation and broken symmetry. At the lowest (mean-field) level of truncation, the formalism degenerates to the well-known Gross-Pitaevskii description of the condensate wave function or one-body order parameter. The treatment is developed in a fully gauge-invariant fashion, and is thereby shown to provide a complete hydrodynamical description, valid in the zero-temperature limit. In particular, by studying the off-diagonal one- and two-body density matrices in terms of the basic ECCM amplitudes, we derive balance (or local conservation) equations for such local observables as the number density, momentum density, and energy density. These are shown to be obeyed not only by the exact untruncated formalism but also by most practical truncation schemes in the ECCM configuration space.