We present the quantum and classical study of a four-well trapped Bose–Einstein condensate (BEC) modeled by the Bose–Hubbard Hamiltonian. The model used is fashioned as a minimal bipartite system consisting of a trimer coupled weakly to a monomer. Semiclassical insights into the fragmentation dynamics of the condensate is obtained by mapping out the Arnold web of the high dimensional classical phase space. A remarkable one-to-one correspondence between the quantum state space in occupation number representation and the classical Arnold web in action space is observed. The relevance of dynamical tunneling for the dynamics of Fock states near resonance junctions on the Arnold web is highlighted. We also predict the possibility of manipulating the transport within the trimer subsystem due to the weak coupling to the monomer.

我们介绍了由 Bose-Hubbard Hamiltonian 建模的四井捕获 Bose-Einstein 凝聚 (BEC) 的量子和经典研究。所使用的模型被塑造成一个最小的二分系统，由一个与单体弱耦合的三聚体组成。通过绘制高维经典相空间的阿诺德网络，可以获得对凝析油碎裂动力学的半经典见解。观察到占用数表示中的量子状态空间与动作空间中的经典阿诺德网络之间存在显着的一一对应关系。强调了动态隧穿与 Arnold 网上共振结附近 Fock 状态动力学的相关性。我们还预测了由于与单体的弱耦合而操纵三聚体子系统内传输的可能性。