Exact solutions of a spin-orbit coupling model in two-dimensional central-potentials and quantum-classical correspondence

TL;DR

This paper explores classical and quantum orbits of a spinning particle in 2D central potentials with spin-orbit coupling, revealing quantum-classical correspondence and fractional angular momentum quantization, leading to a natural emergence of non-Abelian anyons.

Contribution

It provides exact solutions for classical and quantum orbits in a spin-orbit coupled system, demonstrating quantum-classical correspondence and fractional angular momentum quantization.

Findings

Classical and quantum orbits coincide exactly at zero energy.

Quantum wave-functions exhibit fractional angular momentum.

A non-Abelian anyon-model naturally emerges from the system.

Abstract

In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition which leads to an effective non-Abelian gauge field generated by the spin-orbit coupling. Coherent superposition of orbital angular-eigenfunctions obtained explicitly at the condition of zero-energy exhibits the quantum-classical correspondence in the meaning of exact coincidence between classical orbits and spatial patterns of quantum wave-functions, which as a consequence results in the fractional quantization of orbital angular-momentum by the requirement of the same rotational symmetry of quantum and classical orbits. A non-Abelian anyon-model emerges in a natural way.