Dynamics of spinor Bose-Einstein condensate subject to dissipation

We investigate the internal dynamics of the spinor Bose-Einstein Condensates subject to dissipation by solving the Lindblad master equation. It is shown that for the condensates without dissipation its dynamics always evolve along specific orbital in the phase space of ($n_0$, $\theta$) and display three kinds of dynamical properties including Josephson-like oscillation, self-trapping-like oscillation and 'running phase'. In contrast, the condensates subject to dissipation will not evolve along the specific dynamical orbital. If component-1 and component-(-1) dissipate in different rates, the magnetization $m$ will not conserve and the system transits between different dynamical regions. The dynamical properties can be exhibited in the phase space of ($n_0$, $\theta$, $m$).Comment: 5 pages, 3 figure

On the Early In Situ Formation of Pluto's Small Satellites

The formation of Pluto's small satellites - Styx, Nix, Keberos and Hydra - remains a mystery. Their orbits are nearly circular and are near mean-motion resonances and nearly coplanar with Charon's orbit. One scenario suggests that they all formed close to their current locations from a disk of debris that was ejected from the Charon-forming impact before the tidal evolution of Charon. The validity of this scenario is tested by performing $N$-body simulations with the small satellites treated as test particles and Pluto-Charon evolving tidally from an initial orbit at a few Pluto radii with initial eccentricity $e_{\rm C} = 0$ or 0.2. After tidal evolution, the free eccentricities $e_{\rm free}$ of the test particles are extracted by applying fast Fourier transformation to the distance between the test particles and the center of mass of the system and compared with the current eccentricities of the four small satellites. The only surviving test particles with $e_{\rm free}$ matching the eccentricities of the current satellites are those not affected by mean-motion resonances during the tidal evolution in a model with Pluto's effective tidal dissipation function $Q = 100$ and an initial $e_{\rm C}$ = 0.2 that is damped down rapidly. However, these test particles do not have any preference to be in or near 4:1, 5:1 and 6:1 resonances with Charon. An alternative scenario may be needed to explain the formation of Pluto's small satellites.Comment: 27 pages, including 10 figures, accepted for publication in A