2020/01/19 by Peter Schmelcher
Mathematics · Physics and Astronomy · #Anharmonicity #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Degrees of freedom (physics and chemistry) #Dynamics (music) #Geometry #Mathematics #Motion (physics) #Nonlinear Photonic Systems #Nonlinear system #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Saddle #Saddle point #Scattering #Statistical physics #nlin.CD #physics.class-ph
paper · pdf · doi:10.1016/j.cnsns.2020.105599
published as Communications in Nonlinear Science and Numerical Simulation 95, 105599 (2021)
arxiv created 2020/01/19 · openalex publication_date 2020/11/06 · openalex created_date 2020/11/09 · arxiv updated 2021/05/25 · openalex updated_date 2026/08/05
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.