2008/12/09 by Douglas Ballon, Douglas J. Ballon, Henning U. Voss · 42 citations
Chemistry · Engineering · Mathematics · Physics and Astronomy · #Boson #Classical mechanics #Fermion #Geometry #Harmonic #Harmonic oscillator #Harmonics #Invariant (physics) #Mathematics #Mechanical and Optical Resonators #Molecular Junctions and Nanostructures #Physics #Quantum mechanics #Resonator #Ring (chemistry) #Symmetry (geometry) #Synthesis and Properties of Aromatic Compounds #Topology (electrical circuits) #physics.class-ph
paper · pdf · doi:10.1103/physrevlett.101.247701
published in Physical Review Letters 101(24), 247701 (American Physical Society) · Typographic error in Eq. (7) corrected
openalex publication_date 2008/12/09 · arxiv created 2009/08/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 radio frequency resonators constrained to a Möbius 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 rad, 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.