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Two coupled BECs with a large population imbalance exhibit macroscopicquantum self-trapping (MQST) if the ratio of interaction energy to tunnelingenergy is above a critical value. Here we investigate effect of quantumfluctuations on MQST. In particular, we analyze the dynamics of a system of twoelongated Bose gases prepared with a large population imbalance, where due tothe quasi one dimensional character of the gas we no longer have true longrange order, and the effect of quantum fluctuations is much more important. Weshow that MQST is possible in this system, but even when it is achieved it isnot always dynamically stable. Using this instability one can construct stateswith sharply peaked momentum distributions around characteristic momentadependent on system parameters. Our other finding is the nonmonotonicoscillating dependence of the decay rate of the MQST on the length of thewires. We also address the interesting question of thermalization in thissystem and show that it occurs only in sufficiently long wires.

Breakdown of macroscopic quantum self-trapping in coupled mesoscopic one dimensional Bose gases