This material has been published in
Int. J. Modern Physics B
21 (2007), 2324-2334,
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Karl E. Kürten and Christian Krattenthaler
Multistability and multi 2\pi-kinks in the Frenkel-Kontorova model: an application to arrays of Josephson junctions
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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