orbitals has a strong influence in the tunneling dynamics when the trap is displaced. Smerzi and Raghavan researched the coherent atomic tunneling and oscillations between two zero-temperature BECs confined in a double-well magnetic trap in the case of weakly Josephson coupling \[16,17\]. The coupling was provided by a laser barrier in a double well magnetic trap or by Raman coupling between two condensates in different hyperfine levels. The dynamics of phase difference and fractional population imbalance was described with the two-mode nonlinear GPE called as Bose Josephson junction (BJJ) equation. In addition to the nonsinusoidal anharmonic generalization of the ac Josephson effect and plasma oscillations occurring in the superconductor junction (SJJ), the macroscopic quantum self-trapping (MQST, a self-maintained population imbalance with nonzero average value of the fractional population imbalance.) and the $\pi -$phase oscillations ( the time averaged value of the phase difference is equal to $\pi $) were also observed.

In the case of time-dependent trapping potential and non-negative damping and finite temperature effects, the more interesting nonlinear dynamics emerges out, such as chaos. Abdullaev and Kraenkel analyzed the coherent atomic oscillations and resonances between two coupled BECs in a double-well trap with time-dependent tunneling amplitude for different damping 