We study tunneling processes of Bose-Einstein condensate (BEC) on the real time stochastic approach and reveal some properties of their tunneling time. An important result is that the tunneling time decreases as the repulsive interatomic interaction
becomes stronger. Furthermore, the tunneling time in a strong interaction region is not much affected by the potential height and is represented by an almost constant function. We also obtain the other related times such as the hesitating and interaction ones and investigate their dependence on the interaction strength. Finally, we calculate the mean arrival time of BEC wave packet and show the large displacement of its peak position.
We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows a unstable behavior which is called the dynamical instability. The unstable syste
m is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consitent with as those given by the discrete nonlinear Schrodinger equation.
