Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 55, Issue 37, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1751-8121/ac86af
Keywords
classical mechanics; long-range interactions; bifurcations; dipolar interaction
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This study investigates the classical equilibrium properties and metamorphosis of the ground state of interacting dipoles with fixed locations. The dipoles form separate intertwined chains which can be tuned by geometrical parameters, resulting in a self-similar bifurcation diagram linked to the Stern-Brocot tree and the Farey sequence.
We investigate the classical equilibrium properties and metamorphosis of the ground state of interacting dipoles with fixed locations on a helix. The dipoles are shown to align themselves along separate intertwined dipole chains forming single, double, and higher-order helical chains. The number of dipole chains, and their properties such as chirality and length scale on which the chains wind around each other, can be tuned by the geometrical parameters. We demonstrate that all possible configurations form a self-similar bifurcation diagram which can be linked to the Stern-Brocot tree and the underlying Farey sequence. We describe the mechanism responsible for this behavior and subsequently discuss corresponding implications and possible applications.
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