Quantum resonance and anti-resonance for a periodically kicked Bose-Einstein Condensate in a one dimensional Box

We investigate the quantum dynamics of a periodically kicked Bose-Einstein Condensate confined in a one dimensional (1D) Box both numerically and theoretically, emphasizing on the phenomena of quantum resonance and anti-resonance. The quantum resonant behavior of BEC is different from the single particle case but the anti-resonance condition ($T = 2\pi$ and $\alpha = 0$) is not affected by the atomic interaction. For the anti-resonance case, the nonlinearity (atom interaction) causes the transition between oscillation and quantum beating. For the quantum resonance case, because of the coherence of BEC, the energy increase is oscillating and the rate is dramatically affected by the many-body interaction. We also discuss the relation between the quantum resonant behavior and the KAM or non-KAM property of the corresponding classical system.