Abstract
We study the dynamics of a one-dimensional Bose-Einstein condensate located in a time-dependent double-well trapping potential. In particular we investigate the way the system discovers existence of a ground state created in the new deeper well. It was shown that the transfer of the system into the minimum of the potential is triggered by the appearance of the condensate in the new well. Only then the thermal cloud follows the condensed part. During the transfer the eigenvectors of the single-particle density matrix have components localized simultaneously in both wells, which indicates a partial coherence between the two parts of the system.