Classical Möbius-ring resonators exhibit fermion-boson rotational symmetry.

Publication Type	Academic Article
Authors	Ballon D, Voss H
Journal	Phys Rev Lett
Volume	101
Issue	24
Pagination	247701
Date Published	12/09/2008
ISSN	0031-9007
Keywords	Models, Theoretical, Radio Waves
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 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.
DOI	10.1103/PhysRevLett.101.247701
PubMed ID	19113667