Classical Mobius-Ring Resonators Exhibit Fermion-Boson Rotational Symmetry

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.

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References in corpus (4)

• Persistent spin currents in mesoscopic Heisenberg rings
• Lattice with a Twist : Helical Waveguides for Ultracold Matter
• Persistent currents in n-fold twisted Moebius strips
• Fractional flux periodicity of a twisted planar square lattice

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• Topological modes in radiofrequency resonator arrays
• Electronic Structure Trends of Möbius Graphene Nanoribbons from Minimal-Cell Simulations
• Nonlinear topological symmetry protection in a dissipative system
• Topology-induced symmetry breaking demonstrated in antiferromagnetic magnons on a Möbius strip