论文标题
超大的互动和受限制程度的动态展开
Superexponential Interactions and the Dynamical Unfolding of Confined Degrees of Freedom
论文作者
论文摘要
我们探索了一个具有超大相互作用的两体系统，该系统是通往复杂性途径的基本构建块。尽管很简单，这种高度非线性的相互作用产生了许多有趣的特性和丰富的动态。它表现出一个空间区域，其中动力学发生在以横向限制和纵向无界运动为特征的通道中，以及在动力学上渐近不含动力学的两个不同区域。通过两个鞍点的解元过渡将通道中的动力学与渐近自由运动联系起来。散射函数显示出可以用相应的相关图来解释的平稳结构。这些与沿通道的纵向尺寸移动时，与横向运动的非谐度密切相关。我们对鞍点下方和上方的能量的散射过渡进行了全面分析。简要讨论了与多体系统的甲次相互作用的可能变体和扩展。
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.
