On the hydrodynamics of Bose-condensed fluids subject to density-dependent gauge potentials

TL;DR

This paper explores the hydrodynamics of Bose-condensed fluids influenced by density-dependent gauge potentials, revealing nonlinear flow effects, flow-dependent pressure, and the breakdown of Galilean invariance.

Contribution

It introduces a general framework for density-dependent gauge potentials in Bose-condensed fluids, extending to multi-component cases and deriving new flow-dependent terms in the hydrodynamic equations.

Findings

Flow-dependent pressure contribution due to gauge potential

Emergence of a dilation body-force in the momentum equation

Breakdown of Galilean invariance in the nonlinear fluid dynamics

Abstract

When the energy functional of a Bose-condensed state of matter features an effective gauge potential which depends on the density $\rho$ of the condensate, the kinetic energy density of the matter field becomes nonlinear in $\rho$ and additional flow-dependent terms enter the wave equation for the phase of the condensate wavefunction. To begin with, we consider a certain class of density-dependent `single-component' gauge potentials, and later extend this class to encompass more general `multi-component' potentials. The nonlinear flow terms are cast into the general form of an inner-product between the velocity field of the fluid and the gauge potential. This is achieved by introducing a coupling matrix of dimensionless functions $\gamma_{ij}\left( \rho \right)$, which characterises the particular functional form of the gauge potential and regulates the strengths of the nonlinear terms accordingly. In the momentum-transport equation of the fluid, two non-trivial terms emerge due to the density-dependent vector potential. A body-force of dilation appears as a product of the gauge potential and the dilation rate of the fluid, while the fluid stress tensor features a flow-dependent pressure contribution given by the inner-product of the gauge potential and the current density of the fluid. This explicit dependence of the fluid pressure on the flow highlights the lack of Galilean invariance of the nonlinear fluid.