A Class of Exact Solutions For N-Anyons in a N-body Potential

Abstract

A class of exact solutions are obtained for the problem of N-anyons interacting via the N-body potential $V({\vec{x}}_1,{\vec{x}}_2,...,{\vec{x}}_N)$ = $-\frac{e^2}{\sqrt{\frac{1}{N}{\sum }_{i<j}({\vec{x}}_i-{\vec{x}}_j{)}^2}}$ Unlike the oscillator case the resulting spectrum is not linear in the anyon parameter $\alpha (0\le \alpha \le 1)$. However, a la oscillator case, cross-over between the ground states is shown to occur for N-anyons $(N\ge 3)$ experiencing the above potential.

10 pages, no figure, latex file

References in corpus (1)

• Classical Dynamics of Anyons and the Quantum Spectrum

Cited by in corpus (2)

• Properties of size-dependent models having quasiperiodic boundary conditions
• Exact Ground State of Several N-body Problems With an N-body Potential