1999/06/22 by Ghanashyam Date, G. Date, Date, G.
Engineering · Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Condensed Matter (cond-mat) #Elasticity and Wave Propagation #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Numerical methods for differential equations #Quantum chaos and dynamical systems #cond-mat #hep-th #math-ph #math.CA #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/9906018
41 pages, LaTeX, no figures
arxiv created 1999/06/22 · openalex publication_date 1999/06/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
At the classical level anyons with harmonic confinement are known to exhibit two important properties namely partial separability and pseudo-integrability. These stem from the fact that this system is locally identical to isotropic oscillator system but differs in the global topology of the phase space. We clarify the meaning of pseudo-integrability and show that it amounts to a definite reduction of the symmetry group. We elaborate on the role of the fundamental group of the phase space and pseudo-intrgrability in the context of periodic orbit theory and obtain evidence of non-exactly known eigenvalues from the semiclassical trace formula. We also discuss an ambiguity regarding the `half period' trajectories suggested by classical modeling and exhibited by the exactly known propagator for two anyons.