Damped Oscillations of a BEC in a Double-Well Potential

We numerically study the evolution of a one-dimensional Bose gas trapped in a double-well potential below critical temperature. Following ZNG theory$^1$, the coupled dynamics of the condensate and non-condensate is described by the generalized Gross-Pitaevskii equation and the Bolzmann equation respectively. In one dimension the collision integral $C_{22}$ vanishes and only collisions between the condensate and non-condensate ($C_{12}$) are included. The excitations are treated in local density approximation. Initially the non-condensate distribution function is approximated by the local equilibrium Bose distribution. For nonzero temperature the thermodynamical chemical potential is not the same as the eigenvalue of the stationary Gross-Ptaevskii equation. The collision integral $C_{12}$ produces a source term which plays an important role in equilibration processes. \\ 1. E. Zaremba, T. Nikini and A. Griffin. J. Low Temp. Phys. {\bf 116}, 277 (1999).