Dynamics of straight vortex filaments in a BoseEinstein condensate with the Gaussian density profile
Abstract
The dynamics of interacting quantized vortex filaments in a rotating BoseEinstein condensate existing in the ThomasFermi regime at zero temperature and obeying the GrossPitaevskii equation has been considered in the hydrodynamic "nonelastic" approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear secondorder partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a BoseEinstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the longwavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived.
 Publication:

Soviet Journal of Experimental and Theoretical Physics
 Pub Date:
 June 2017
 DOI:
 10.1134/S1063776117050041
 arXiv:
 arXiv:1612.00165
 Bibcode:
 2017JETP..124..932R
 Keywords:

 Condensed Matter  Quantum Gases;
 Nonlinear Sciences  Pattern Formation and Solitons;
 Physics  Fluid Dynamics
 EPrint:
 revtex, 10 pages, 7 figures, Introduction improved, English translation of Russian text accepted to JETP