方形软洛伦兹气体中的反常扩散
Anomalous Diffusion in the Square Soft Lorentz Gas
AI总结：
研究方形软洛伦兹气体的正常与反常扩散，提出单胞跳跃模型并结合相空间和参数空间结构，刻画硬台球到软势转变中的动力学变化。
摘要：
我们展示并分析了二维系统中点状粒子的反常扩散特性；该系统中的圆形散射体按方形晶格排列，并由光滑势控制，称为方形软洛伦兹气体。数值模拟揭示，正常扩散与反常扩散之间存在依赖于系统参数的丰富相互作用。为描述正常区域中的扩散，我们建立了单胞跳跃模型；在单跳极限下，该模型恢复 Machta-Zwanzig 近似，并随跳跃次数增加而收敛到数值扩散系数。反常扩散的特征是相空间中形成 Kolmogorov-Arnold-Moser 岛的准弹道轨道，同时参数空间中存在由散射体间距和势软度定义的复杂舌状结构。粒子位移矢量分布与硬壁方形洛伦兹气体的解析和数值结果表现出显著相似性：正常扩散时呈高斯行为，反常区域中则因准弹道轨道而具有长尾。因此，本工作提供了一份关键动力学系统性质目录，用以刻画从硬台球到软势转变时扩散的复杂变化。
英文摘要：
We demonstrate and analyze anomalous diffusion properties of point-like particles in a two-dimensional system with circular scatterers arranged in a square lattice and governed by smooth potentials, referred to as the square soft Lorentz gas. Our numerical simulations reveal a rich interplay of normal and anomalous diffusion depending on the system parameters. To describe diffusion in normal regimes, we develop a unit cell hopping model that, in the single-hop limit, recovers the Machta-Zwanzig approximation and converges toward the numerical diffusion coefficient as the number of hops increases. Anomalous diffusion is characterized by quasiballistic orbits forming Kolmogorov-Arnold-Moser islands in phase space, alongside a complex tongue structure in parameter space defined by the interscatterer distance and potential softness. The distributions of the particle displacement vector show notable similarities to both analytical and numerical results for a hard-wall square Lorentz gas, exhibiting Gaussian behavior in normal diffusion and long tails due to quasiballistic orbits in anomalous regimes. Our work thus provides a catalog of key dynamical system properties that characterize the intricate changes in diffusion when transitioning from hard billiards to soft potentials.
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