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

Bose-Einstein condensates in a double-well trap, as well 3He-B baths connected by micropores, have been shown to exhibit Josephson-like tunneling phenomena.,Unlike the superconductor,Josephson junction of phase difference 4> that maps onto a rigid pendulum of energy cos(4>), these systems map onto a momentum- shortened pendulum of energy -Jl-pfCosify and length yj\-p% where pj, 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, { = 0 = p^, state that are characteristic dynamic signatures of