are localized on one of the condensates. However, for large enough $\Delta E_{1}$ $(1.700)$, the chaotic sea is symmetrical to $z=0$. This indicates that, in the completely chaotic oscillation, the time-averaged value of the fractional population imbalance is zero, and the long-lived MQST or localization disappears.

The completely chaotic oscillations of the fractional population imbalance from Rabi oscillation and MQST are presented in Fig. 7. The left column corresponds to $z(0)=0.5$, $\phi (0)=0.0$, $\Delta E_{0}=0.0$, $\Lambda
=10.0 $, $\omega =4\pi $, $\Delta E_{1}=7.500$ and $\eta =0.0$, the right column corresponds to $z(0)=0.75$, $\phi (0)=0.0$, $\Delta E_{0}=0.0$, $%
\Lambda =10.0$, $\omega =2\pi $, $\Delta E_{1}=1.700$ and $\eta =0.0$. The first row is the time evolution of $z$, the second row is the power spectra of the corresponding oscillation. Apparently, through the tunnel of Rabi oscillation, the short-term localization or MQST can be changed from one of the BECs to the other, and the corresponding power spectra is continuous.

Because of the existence of the damping, the dimensionless system is not a Hamiltonian system but a dissipative system and the volume in phase space will decrease through time evolution. Factually, these effects are the basic reason for the complex oscillation behavior. A 