Part E SuperconductivityNo Access

MULTISTABILITY AND MULTI 2π-KINKS IN THE FRENKEL–KONTOROVA MODEL: AN APPLICATION TO ARRAYS OF JOSEPHSON JUNCTIONS

KARL E. KÜRTEN

Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, A-1090 WIEN, Austria

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and

CHRISTIAN KRATTENTHALER

Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A-1090 Vienna, Austria

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https://doi.org/10.1142/S0217979207043695Cited by:2 (Source: Crossref)

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 r^N/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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