Bose-condensate tunneling dynamics: Momentum-shortened pendulum with damping

Bose-Einstein condensates in a double-well trap, as well He-3-B baths connected by micropores, have been shown to exhibit Josephson-like tunneling phenomena. Unlike the superconductor Josephson junction of phase difference phi that maps onto a rigid pendulum of energy cos(phi), these systems map onto a momentum-shortened pendulum of energy -root 1-p(phi)(2)cos(phi) and length root 1-p(phi)(2), where p(phi) is a population imbalance between the wells/baths. We study here the effect of damping on the four distinct modes of the nonrigid pendulum, characterized by distinct temporal mean values, [phi] and [p(phi)]. Damping is shown to produce different decay trajectories to the final equilibrium phi=0=p(phi) state that are characteristic dynamic signatures of the initial oscillation modes. In particular, damping causes pi-state oscillations with [phi]=pi to increase in amplitude and pass through phase-slip states, before equilibrating. Similar behavior has been seen in He-3-B experiments. [S1050-2947(99)03207-2].