Superfluid vortex multipoles and soliton stripes on a torus
arXiv:2201.11054 · doi:10.1103/PhysRevA.105.063325
Abstract
We study the existence, stability, and dynamics of vortex dipole and quadrupole configurations in the nonlinear Schrödinger (NLS) equation on the surface of a torus. For this purpose we use, in addition to the full two-dimensional NLS on the torus, a recently derived [Phys. Rev. A 101, 053606 (2021)] reduced point-vortex particle model which is shown to be in excellent agreement with the full NLS evolution. Horizontal, vertical, and diagonal stationary vortex dipoles are identified and continued along the torus aspect ratio and the chemical potential of the solution. Windows of stability for these solutions are identified. We also investigate stationary vortex quadrupole configurations. After eliminating similar solutions induced by invariances and symmetries, we find a total of 16 distinct configurations ranging from horizontal and vertical aligned quadrupoles, to rectangular and rhomboidal quadrupoles, to trapezoidal and irregular quadrupoles. The stability for the least unstable and, potentially, stable quadrapole solutions is monitored both at the NLS and the reduced model levels. Two quadrupole configurations are found to be stable on small windows of the torus aspect ratio and a handful of quadrupoles are found to be very weakly unstable for relatively large parameter windows. Finally, we briefly study the dark soliton stripes and their connection, through a series of bifurcation cascades, with steady state vortex configurations.
18 pages, 24 figures, movies available at: https://carretero.sdsu.edu/ [Publications]
References in corpus (9)
- Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
- Formation of bright matter-wave solitons during the collapse of Bose-Einstein condensates
- Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
- Experimental observation of oscillating and interacting matter wave dark solitons
- Stationary and non-stationary fluid flow of a Bose-Einstein condensate through a penetrable barrier
- Observation of ultracold atomic bubbles in orbital microgravity
- Thermodynamics in expanding shell-shaped Bose-Einstein condensates
- Quantized superfluid vortex dynamics on cylindrical surfaces and planar annuli
- Superfluid Vortex Dynamics on Planar Sectors and Cones