Macroscopic quantum tunneling and resonances in coupled Bose-Einstein   condensates with oscillating atomic scattering length
  We study the macroscopic quantum tunneling, self-trapping phenomena in two weakly coupled Bose-Einstein condensates with periodically time-varying atomic scattering length.   The resonances in the oscillations of the atomic populations are investigated. We consider oscillations in the cases of macroscopic quantum tunneling and the self-trapping regimes. The existence of chaotic oscillations in the relative atomic population due to overlaps between nonlinear resonances is showed. We derive the whisker-type map for the problem and obtain the estimate for the critical amplitude of modulations leading to chaos. The diffusion coefficient for motion in the stochastic layer near separatrix is calculated. The analysis of the oscillations in the rapidly varying case shows the possibilty of stabilization of the unstable Pi-mode regime. 
F. Kh. Abdullaev and R. A. Kraenkel