This material has been published in Int. J. Modern Physics B 21 (2007), 2324-2334, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by World Scientific. This material may not be copied or reposted without explicit permission.

Karl E. Kürten and Christian Krattenthaler

Multistability and multi 2\pi-kinks in the Frenkel-Kontorova model: an application to arrays of Josephson junctions

(11 pages)

Abstract. A regular ring of Josephson junctions, connected in parallel, is studied analytically and numerically. We show that, depending on the strength of the r-well cosine potential the energy landscape of the Hamiltonian can have of the order of rN/N locally stable minima separated by large barriers specified by unstable saddle points. The counting problem for the degeneracy of the total energy is equivalent to a wellknown necklace problem in combinatorial mathematics. We also demonstrate that the distribution of the phase differences as well as the energy spectrum is fractal provided that the strength of the cosine potential is sufficiently strong.

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