Quantum Fluid Dynamics: An Extended Coupled Cluster Treatment

Abstract

The extended coupled cluster method (ECCM) is applied to the zero-temperature condensed Bose fluid for the general case of a non-uniform and time-dependent condensate wavefunction. The principal aim is to derive the appropriate balance equations of fluid dynamics for such local observables as the number density, current density and energy density. This is achieved by coupling the system to scalar and vector gauge fields, so that the theory may be formulated in a completely gauge-invariant fashion to take fully into account the underlying U(l) symmetry imposed by number conservation. The ECCM formalism is based on the equations of motion for a set of linked-cluster amplitudes which characterise the system completely. The off-diagonal one- and two-body density matrices are studied in terms of these amplitudes, and the various balance equations of fluid dynamics are thereby derived. Furthermore, we show how these are also exactly satisfied by most practical approximation schemes applied to the otherwise exact ECCM description. The fact that the ECCM amplitudes all strictly obey the cluster property, further implies that our gauge-invariant formalism is capable in principle of a complete fluid-dynamical description of the system at zero temperature, including possible states of topological excitation or deformation and of broken symmetry.