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arXiv · 2001.07705

Superexponential Interactions and the Dynamical Unfolding of Confined Degrees of Freedom

Peter Schmelcher
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Abstract

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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Peter Schmelcher. 2020-01-19. Superexponential Interactions and the Dynamical Unfolding of Confined Degrees of Freedom. https://doi.org/10.1016/j.cnsns.2020.105599

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