Anyons beyond the plane

TL;DR

This paper explores how particles in three-dimensional space can exhibit anyon-like behavior when they have a probability of being in a planar region with Aharonov-Bohm interactions, revealing new mechanisms for anyon formation.

Contribution

It demonstrates that planar motion of particles in 3D can be effectively anyon-like, with a statistical parameter linked to the probability of being in a plane, and shows bound states of charge-flux composites behaving as anyons.

Findings

Planar motion is anyon-like with a parameter proportional to the probability squared.

Charge-flux fermionic composites can form bound states acting as anyons.

No external potential is needed for these bound states to behave as anyons.

Abstract

We consider particles in three-dimensional space, which have a certain probability to find themselves in a thin layer (``plane''), where they are assumed to be well described by a planar Hamiltonian and are subject to Aharonov-Bohm-type interaction. We demonstrate that their planar motion is then anyonlike, with the ``effective statistical parameter'' proportional essentially to the square of the probability. We also show that charge-flux composites with solenoids of finite length, provided they are themselves fermions, can form a bound state in which they behave like anyons, without any external potential confining them to a plane.