Cherenkov radiation from fluxon in a stack of coupled long Josephson junctions

We present a systematic study of the Cherenkov radiation of Josephson plasma waves by fast moving fluxon in a stack of coupled long Josephson junctions for different fluxon modes. It is found that at some values of parameters current-voltage characteristic may exhibit a region of the back-bending on the fluxon step. In the opposite limit the emission of the Cherenkov radiation takes place. In the annular junctions of moderate length the interaction of the emitted waves with fluxon results in the novel resonances which emerge on the top of the fluxon step. We present more exact formulas which describe the position of such resonances taking into account difference between junction and non-linear corrections. The possibility of direct detection of the Cherenkov radiation in junctions of linear geometry is discussed.Comment: 10 pages, 12 figures, accepted to JLT

Limiting Distribution of Frobenius Numbers for n=3n=3

The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers outlined in earlier work of J. Bourgain and Ya. Sinai and fill some gaps formulated there as hypotheses.Comment: 13 page

AC induced damping of a fluxon in long Josephson junction

We present a theoretical and experimental study of Josephson vortex (fluxon) moving in the presence of spatially homogeneous dc and ac bias currents. By mapping this problem to the problem of calculating the current-voltage characteristic of a small Josephson junction, we derive the dependence of the average fluxon velocity on the dc bias current. In particular we find that the low frequency ac bias current results in an additional nonlinear damping of fluxon motion. Such ac induced damping crucially depends on the intrinsic damping parameter and increases drastically as this parameter is reduced. We find a good agreement of the analysis with both the direct numerical simulations and the experimentally measured current-voltage characteristics of a long annular Josephson junction with one trapped fluxon.Comment: Physical Review B, in pres

Observation of progressive motion of ac-driven solitons

We report the first experimental observation of phase-locked motion of a topological soliton at a nonzero average velocity in a periodically modulated lossy medium, under the action of an ac force with no dc component [the effect was predicted by G. Filatrella, B.A. Malomed, and R.D. Parmentier, Phys. Lett. A 198, 43 (1995)]. The velocity is related by a resonant condition to the driving frequency. The observation is made in terms of the current-voltage, I(V), characteristics for a fluxon trapped in an annular Josephson junction placed into dc magnetic field. Large zero-crossing constant-voltage steps, exactly corresponding to the resonantly locked soliton motion at different orders of the resonance, are found on the experimental I(V) curves. A measured dependence of the size of the steps vs. the external magnetic field is in good agreement with predictions of an analytical model based on the balance equation for the fluxon's energy. The effect has a potential application as a low-frequency voltage standard. The work was supported by a grant from the German-Israeli Foundation.Comment: Physical Review B, in press (Rapid Communication