一维量子液滴的统计力学
Statistical mechanics of one-dimensional quantum droplets
摘要：
研究了由修正的Gross-Pitaevskii方程描述的调制不稳定的一维量子液滴的统计力学和动力学弛豫过程。为了确定其经典的配分函数，我们利用半解析传递积分算子（TIO）技术。后者预测了所观察到的波函数振幅的分布，并产生两点关联函数，提供了深入了解涉及量子液滴的涌现动力学。我们比较随后的TIO结果与调制不稳定动力学的大时间获得的概率分布，以及与适当构造的朗之万动力学的平衡性质。我们发现，不稳定性导致自发形成的量子液滴具有多个碰撞，并发现在大的演化时间合并。我们的结果，从不同的方法是在良好的协议，除了在特殊的限制，液滴加宽的低温的情况下。在此限制下，分布获得一个明显的双峰字符，表现出TIO解决方案和朗之万动力学之间的偏差。
英文摘要：
We study the statistical mechanics and the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets described by a modified Gross-Pitaevskii equation. To determine the classical partition function thereof, we leverage the semi-analytical transfer integral operator (TIO) technique. The latter predicts a distribution of the observed wave function amplitudes and yields two-point correlation functions providing insights into the emergent dynamics involving quantum droplets. We compare the ensuing TIO results with the probability distributions obtained at large times of the modulationally unstable dynamics as well as with the equilibrium properties of a suitably constructed Langevin dynamics. We find that the instability leads to the spontaneous formation of quantum droplets featuring multiple collisions and by which are found to coalesce at large evolution times. Our results from the distinct methodologies are in good agreement aside from the case of low temperatures in the special limit where the droplet widens. In this limit, the distribution acquires a pronounced bimodal character, exhibiting a deviation between the TIO solution and the Langevin dynamics.
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