超指数相互作用与有限自由度的动力学展开
Superexponential Interactions and the Dynamical Unfolding of Confined Degrees of Freedom
摘要：
我们探索了一个两体系统与超指数的相互作用，作为一个基本的构建块的路线复杂性。虽然是惊人的简单，这种高度非线性的相互作用产生了大量的有趣的属性和丰富的动力学。它表现出一个空间区域的动态发生在一个通道，其特征在于由一个横向限制和纵向无界的运动和另外两个不同的区域，其中的动态是渐近自由的。通过两个鞍点的解除限制过渡连接的动态通道中的渐近自由运动。散射函数显示平台和峰值结构，可以解释在相应的相关图。这些都是密切相关的横向运动，而沿着通道的纵向尺寸移动的变化的非谐性。我们执行一个全面的分析的散射过渡的能量低于和高于鞍点。简要讨论了超指数相互作用在多体系统中的可能变体和扩展。
英文摘要：
We explore a two-body system with superexponential interactions that serves as a fundamental building block for a route to complexity. While being of striking simplicity this highly nonlinear interaction yields a plethora of intriguing properties and a rich dynamics. It exhibits a spatial region where the dynamics occurs in a channel characterised by a transversally confined and longitudinally unbounded motion and additionally two distinct regions where the dynamics is asymptotically free. A deconfinement transition via two saddle points connects the dynamics in the channel with the asymptotically free motion. The scattering functions show plateau and peak structures that can be interpreted in terms of corresponding correlation diagrams. These are intimately related to the varying anharmonicity of the transverse motion while moving along the longitudinal dimension of the channel. We perform a comprehensive analysis of the scattering transition for energies below and above the saddle points. Possible variants and extensions of the superexponential interaction to many-body system are briefly discussed.
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