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

TL;DR

This paper derives exact solutions for N-anyon systems under a specific N-body potential, revealing non-linear spectra and ground state cross-overs, advancing understanding of anyonic interactions in many-body quantum systems.

Contribution

It introduces a new class of exact solutions for N-anyon systems with a novel N-body potential, highlighting spectral properties and ground state transitions.

Findings

Spectrum is non-linear in the anyon parameter α.

Ground state cross-over occurs for N ≥ 3.

Exact solutions are obtained for the specified N-body potential.

Abstract

A class of exact solutions are obtained for the problem of N-anyons interacting via the N-body potential $V (\vec x_1,\vec x_2,...,\vec x_N)$ = $-{e^2\over\sqrt{{1\over N}\sum_{i<j} (\vec x_i-\vec x_j)^2}}$ Unlike the oscillator case the resulting spectrum is not linear in the anyon parameter $\alpha (0\leq \alpha\leq 1)$. However, a la oscillator case, cross-over between the ground states is shown to occur for N-anyons $(N\geq 3)$ experiencing the above potential.