Nonrelativistic anyons in external electromagnetic field

TL;DR

This paper extends nonrelativistic anyon models to include arbitrary electromagnetic fields, revealing Hall-like motion at critical fields and uncovering nonlocality and phase distinctions in quantum spectra.

Contribution

It generalizes first-order infinite-component field equations for nonrelativistic anyons to arbitrary electromagnetic backgrounds, introducing consistent coupling and analyzing quantum spectral properties.

Findings

At critical magnetic field, particles follow Hall-like motion.

Inhomogeneous magnetic fields induce hidden nonlocality in the quantum system.

Spectral and state structure vary with magnetic field, indicating distinct phases.

Abstract

The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic fields. Consistent coupling of the underlying classical system to arbitrary fields is introduced; at a critical value of the magnetic field, the particle follows a Hall-like law of motion. The corresponding quantized system reveals a hidden nonlocality if the magnetic field is inhomogeneous. In the quantum Landau problem spectral as well as state structure (finite vs. infinite) asymmetry is found. The bound and scattering states, separated by the critical magnetic field phase, behave as further, distinct phases.