2014/09/18 by A. V. Zampetaki, J. Stockhofe, P. Schmelcher +1 · 18 citations
Chemistry · Mathematics · Physics and Astronomy · #Bifurcation #Bifurcation theory #Chemistry #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Degeneracy (biology) #Geometry #Helix (gastropod) #Mathematics #Mechanical and Optical Resonators #Molecular physics #Nonlinear Photonic Systems #Oscillation (cell signaling) #Physics #Pitchfork bifurcation #Quantum mechanics #RADIUS #Zigzag #cond-mat.other #physics.atom-ph
paper · pdf · doi:10.1103/physreva.91.023409
published in Physical Review A 91(2) (American Physical Society) · 4 pages, 3 figures
arxiv created 2014/09/18 · openalex publication_date 2015/02/10 · arxiv updated 2015/02/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Constraining long-range interacting particles to move on a curved manifold can drastically alter their effective interactions. As a prototype we explore the structure and vibrational dynamics of crystalline configurations formed on a closed helix. We show that the ground state undergoes a pitchfork bifurcation from a symmetric polygonic to a zigzag-like configuration with increasing radius of the helix. Remarkably, we find that, for a specific value of the helix radius, below the bifurcation point, the vibrational frequency spectrum collapses to a single frequency. This allows for an essentially independent small-amplitude motion of the individual particles and, consequently, localized excitations can propagate in time without significant spreading. Upon increasing the radius beyond the degeneracy point, the band structure is inverted, with the out-of-phase oscillation mode becoming lower in frequency than the mode corresponding to the center-of-mass motion.