无序晶格中无热化的混沌性
Chaoticity without thermalisation in disordered lattices
摘要：
我们研究了无序晶格中玻色-爱因斯坦凝聚体的混沌性和热化现象，用离散的非线性薛定谔方程（DNLS）描述。辛积分方法使我们能够准确地获得完整的相空间轨迹和它们的最大李雅普诺夫指数（mLEs），表征其混沌性。我们发现，无序破坏遍历性相空间分解成子系统，有效地不相交的实验相关的时间尺度上，即使精力充沛，经典本地化不能发生。这使我们得出结论，mLE是一个非常差的遍历性指标，因为它是不敏感的轨迹被限制在相空间的一个子区域。无序晶格中BEC的最终热化不能仅仅根据其相空间轨迹的混沌性来预测。
英文摘要：
We study chaoticity and thermalization in Bose-Einstein condensates in disordered lattices, described by the discrete nonlinear Schrödinger equation (DNLS). A symplectic integration method allows us to accurately obtain both the full phase space trajectories and their maximum Lyapunov exponents (mLEs), which characterize their chaoticity. We find that disorder destroys ergodicity by breaking up phase space into subsystems that are effectively disjoint on experimentally relevant timescales, even though energetically, classical localisation cannot occur. This leads us to conclude that the mLE is a very poor ergodicity indicator, since it is not sensitive to the trajectory being confined to a subregion of phase space. The eventual thermalization of a BEC in a disordered lattice cannot be predicted based only on the chaoticity of its phase space trajectory.
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