Abstract
Point masses moving in 2+1 dimensions draw out braids in space-time. If they move under the influence of some pairwise potential, what braid types are possible? By starting with fictional paths of the desired topology and ``relaxing'' them by minimizing the action, we explore the braid types of potentials of the form V\ensuremath{\propto}${\mathit{r}}^{\mathrm{\ensuremath{\alpha}}}$ from \ensuremath{\alpha}\ensuremath{\le}-2, where all braid types occur, to \ensuremath{\alpha}=2, where the system is integrable. We also discuss issues of symmetry and stability. We propose this kind of topological classification as a tool for extending the ``symbolic dynamics'' approach to many-body dynamics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
