Gros-Pitaevskii晶格中的弱非遍历动力学
Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
摘要：
微正则Gros-Pitaevskii（又名半经典玻色-哈伯德）晶格模型动力学的特征在于一对能量和范数密度。巨正则吉布斯分布由于其动能谱的有界性而不能描述密度空间的一部分。我们定义庞加莱平衡流形和计算统计的微正则偏移时间。分布函数的尾部量化了多体动力学到弱非遍历相的接近程度，这发生在平均漂移时间为无穷大时。我们发现，交叉到弱非遍历动力学发生在非吉布斯阶段内，被忽视的最大李雅普诺夫指数。在非吉布斯阶段的遍历部分，吉布斯分布应被替换为一个未知的修改。我们将我们的研究结果与相应的可积极限，接近该极限的行动是通过一个短程耦合网络相互作用。
英文摘要：
The microcanonical Gross--Pitaevskii (aka semiclassical Bose-Hubbard) lattice model dynamics is characterized by a pair of energy and norm densities. The grand canonical Gibbs distribution fails to describe a part of the density space, due to the boundedness of its kinetic energy spectrum. We define Poincare equilibrium manifolds and compute the statistics of microcanonical excursion times off them. The tails of the distribution functions quantify the proximity of the many-body dynamics to a weakly-nonergodic phase, which occurs when the average excursion time is infinite. We find that a crossover to weakly-nonergodic dynamics takes place inside the nonGibbs phase, being unnoticed by the largest Lyapunov exponent. In the ergodic part of the non-Gibbs phase, the Gibbs distribution should be replaced by an unknown modified one. We relate our findings to the corresponding integrable limit, close to which the actions are interacting through a short range coupling network.
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