Classical Mobius-Ring Resonators Exhibit Fermion-Boson Rotational Symmetry

TL;DR

This paper shows that classical M"obius-ring resonators exhibit a unique fermion-like rotational symmetry, producing half-integer harmonics that are invariant under 4pi rotations, unlike traditional ring resonators.

Contribution

It demonstrates that M"obius topology in classical resonators leads to fermion-like rotational symmetry and half-integer harmonics, expanding understanding of symmetry in classical systems.

Findings

M"obius resonators produce half-integer harmonics.

Half-integer harmonics are invariant under 4pi rotations.

Results suggest new pathways for materials and instrumentation design.

Abstract

The behavior of coupled harmonic oscillators in systems with specified boundary conditions is typically characterized by resonances whose frequency spectra represent harmonics according to properties of the individual oscillators, the interactions between them, and the overall symmetry of the system. Here it is demonstrated that classical one- and two-dimensional radiofrequency resonators constrained to a Mobius topology are the formal partners of cylindrical ring resonators, and specifically give rise to half-integral harmonic excitations that are orthogonal to the integral excitations of a ring. In particular, the half-integral harmonics are formally invariant under rotations at a minimum of 4pi rather than 2pi radians, in analogy to the rotational symmetry of fermions in quantum mechanics. The results offer a pathway for discovery in other physical systems as well as the design of novel materials and electronic instrumentation.