In a recent experiment, Kwon et. al (arXiv:1403.4658 [cond-mat.quant-gas]) generated a disordered state of quantum vortices by translating an oblate Bose-Einstein condensate past a laserinduced obstacle and studied the subsequent decay of vortex number. Using mean-field simulations of the Gross-Pitaevskii equation, we shed light on the various stages of the observed dynamics. We find that the flow of the superfluid past the obstacle leads initially to the formation of a classical-like wake, which later becomes disordered. Following removal of the obstacle, the vortex number decays due to vortices annihilating and drifting to the boundary. Our results are in excellent agreement with the experimental observations. Furthermore, we probe thermal effects through phenomenological dissipation.

Abstract. We show that an elliptical obstacle moving through a Bose-Einstein condensate generates wakes of quantum vortices which resemble those of classical viscous flow past a cylinder or sphere. The role of ellipticity is to facilitate the interaction of the vortices nucleated by the obstacle. Initial steady symmetric wakes lose their symmetry and form clusters of like-signed vortices, in analogy to the classical Bénard-von Kármán vortex street. Our findings, demonstrated numerically in both two and three dimensions, confirm the intuition that a sufficiently large number of quanta of circulation reproduce classical physics.arXiv:1401.4041v2 [cond-mat.quant-gas]

We model the superfluid flow of liquid helium over the rough surface of a wire (used to experimentally generate turbulence) profiled by atomic force microscopy. Numerical simulations of the Gross-Pitaevskii equation reveal that the sharpest features in the surface induce vortex nucleation both intrinsically (due to the raised local fluid velocity) and extrinsically (providing pinning sites to vortex lines aligned with the flow). Vortex interactions and reconnections contribute to form a dense turbulent layer of vortices with a nonclassical average velocity profile which continually sheds small vortex rings into the bulk. We characterize this layer for various imposed flows. As boundary layers conventionally arise from viscous forces, this result opens up new insight into the nature of superflows.

Using the classical field method, we study numerically the characteristics and decay of the turbulent tangle of superfluid vortices which is created in the evolution of a Bose gas from highly nonequilibrium initial conditions. By analysing the vortex line density, the energy spectrum and the velocity correlation function, we determine that the turbulence resulting from this effective thermal quench lacks the coherent structures and the Kolmogorov scaling; these properties are typical of both ordinary classical fluids and of superfluid helium when driven by grids or propellers. Instead, thermal quench turbulence has properties akin to a random flow, more similar to another turbulent regime called ultra-quantum turbulence which has been observed in superfluid helium.

We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-Émery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the Möbius ladders. We also highlight an online tool for calculating the curvature of graphs under several variants of the curvature notions that we use in the classification. As a consequence of the classification result we show that non-negatively curved cubic expanders do not exist.arXiv:1712.03033v2 [math.CO]