Classical Dynamics of Anyons and the Quantum Spectrum

TL;DR

This paper demonstrates that all known exact solutions for N-anyons in an oscillator potential originate from collective degrees of freedom and that the system is pseudo-integrable, making the solutions thermodynamically and dynamically trivial.

Contribution

It reveals that the exact solutions are derived from collective modes and shows the system's pseudo-integrability, providing new insights into anyon dynamics.

Findings

All exact solutions arise from collective degrees of freedom

The system is pseudo-integrable as per Richens and Berry

Solutions are thermodynamically and dynamically trivial

Abstract

In this paper we show that (a) all the known exact solutions of the problem of N-anyons in oscillator potential precisely arise from the collective degrees of freedom, (b) the system is pseudo-integrable ala Richens and Berry. We conclude that the exact solutions are trivial thermodynamically as well as dynamically.