We consider the classical dynamics of a particle in a one-dimensional space-periodic potential U(X) = U(X+2pi) under the influence of a time-periodic space-homogeneous external field E(t) = E(t+T). If E(t) is neither a symmetric function of t nor antisymmetric under time shifts E(t+/-T/2) not equal-E(t), an ensemble of trajectories with zero current at t = 0 yields a nonzero finite current as t-->infinity. We explain this effect using symmetry considerations and perturbation theory. Finally we add dissipation (friction) and demonstrate that the resulting set of attractors keeps the broken symmetry property in the basins of attraction and leads to directed currents as well.

We report on the observation of spatially-localized excitations in a ladder of small Josephson junctions. The excitations are whirling states which persist under a spatially-homogeneous force due to the bias current. These states of the ladder are visualized using a low temperature scanning laser microscopy. We also compute breather solutions with high accuracy in corresponding model equations. The stability analysis of these solutions is used to interpret the measured patterns in the I − V characteristics.The present decade has been marked by an intense theoretical research on dynamical localization phenomena in spatially discrete systems, namely on discrete breathers (DB). These exact solutions of the underlying equations of motion are characterized by periodicity in time and localization in space. Away from the DB center the system approaches a stable (typically static) equilibrium. (For reviews see [1], [2]). These solutions are robust to changes of the equations of motion, exist in translationally invariant systems and any lattice dimension. Discrete breathers have been discussed in connection with a variety of physical systems such as large molecules, molecular crystals [3], spin lattices [4,5], to name just a few.For a localized excitation such as a DB, the excitation of plane waves which might carry the energy away from the DB does not occur due to the spatial discreteness of the system. The discreteness provides a cutoff for the wave length of plane waves and thus allows to avoid resonances of all temporal DB harmonics with the plane waves. The nonlinearity of the equations of motion is needed to allow for the tuning of the DB frequency [1].Though the DB concept was initially developed for conservative systems, it can be easily extended to dissipative systems [6]. There discrete breathers become timeperiodic spatially localized attractors, competing with other (perhaps nonlocal) attractors in phase space. The characteristic property of DBs in dissipative systems is that these localized excitations are predicted to persist under the influence of a spatially homogeneous driving force. This is due to the fact, that the driving force compensates the dissipative losses of the DB.So far research in this field was predominantly theoretical. Identifying and analyzing of experimental systems for the direct observation of DBs thus becomes a very actual and challenging problem. Experiments on localization of light propagating in weakly coupled optical waveguides [7], low-dimensional crystals [8] and antiferromagnetic materials [9] have been recently reported. In this work we realize the theoretical proposal [10] to observe DB-like localized excitations in arrays of coupled Josephson junctions. A Josephson junction is formed between two superconducting islands. Each island is characterized by a macroscopic wave function Ψ ∼ e iθ of the superconducting state. The dynamics of the junction is described by the time evolution of the gauge-invariant phase difference ϕ = θ 2 − θ 1 − 2π Φ0A · ds between adjacent islands. H...

The ratchet dynamics of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least bi-harmonic) of zero mean is studied. The dependence of the kink mean velocity on system parameters is investigated numerically and the results are compared with a perturbation analysis based on a point particle representation of the soliton. We find that first order perturbative calculations lead to incomplete descriptions, due to the important role played by the soliton-phonon interaction in establishing the phenomenon. The role played by the temporal symmetry of the system in establishing soliton ratchets is also emphasized. In particular, we show the existence of an asymmetric internal mode on the kink profile which couples to the kink translational mode through the damping in the system. Effective soliton transport is achieved when the internal mode and the external force get phase locked. We find that for kinks driven by bi-harmonic drivers consisting of the superposition of a fundamental driver with its first odd harmonic, the transport arises only due to this internal mode mechanism, while for bi-harmonic drivers with even harmonic superposition, also a point-particle contribution to the drift velocity is present. The phenomenon is robust enough to survive the presence of thermal noise in the system and can lead to several interesting physical applications.

Experimental observation of the unidirectional motion of a topological soliton driven by a biharmonic ac force of zero mean is reported. The observation is made by measuring the current-voltage characteristics for a fluxon trapped in an annular Josephson junction that was placed into a microwave field. The dependence of the fluxon mean velocity at zero dc bias versus the phase shift between the first and second harmonic of the driving force is in qualitative agreement with theoretical expectations.