Hydrodynamics of nonlinear gauge-coupled quantum fluids
- URL: http://arxiv.org/abs/2012.13834v1
- Date: Sat, 26 Dec 2020 23:59:12 GMT
- Title: Hydrodynamics of nonlinear gauge-coupled quantum fluids
- Authors: Y. Buggy, L.G. Phillips and P. \"Ohberg
- Abstract summary: We show that the occurrence of an arbitrary density-dependent gauge potential in the meanfield Hamiltonian of a Bose-condensed fluid invariably leads to nonlinear flow-dependent terms.
By numerical simulation, we illustrate an interesting effect of the nonlinear gauge potential on the groundstate wavefunction of a superfluid in the presence of a foreign impurity.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: By constructing a hydrodynamic canonical formalism, we show that the
occurrence of an arbitrary density-dependent gauge potential in the meanfield
Hamiltonian of a Bose-condensed fluid invariably leads to nonlinear
flow-dependent terms in the wave equation for the phase, where such terms arise
due to the explicit dependence of the mechanical flow on the fluid density. In
addition, we derive a canonical momentum transport equation for this class of
nonlinear fluid and obtain an expression for the stress tensor. Further, we
study the hydrodynamic equations in a particular nonlinear fluid, where the
effective gauge potential results from the introduction of weak contact
interactions in an ultracold dilute Bose gas of optically-addressed two-level
atoms. In the Cauchy equation of mechanical momentum transport of the
superfluid, 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 stress tensor features a
canonical flow pressure term given by the inner-product of the gauge potential
and the canonical current density. By numerical simulation, we illustrate an
interesting effect of the nonlinear gauge potential on the groundstate
wavefunction of a superfluid in the presence of a foreign impurity. We find
that the groundstate adopts a non-trivial local phase, which is antisymmetric
under reversal of the gauge potential. The phase profile leads to a
canonical-flow or phase-flow dipole about the impurity, resulting in a skirting
mechanical flow. As a result, the pressure becomes asymmetric about the object
and the condensate undergoes a deformation.
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