Fractional vortex in asymmetric 0-π\pi long Josephson junctions

We consider an infinitely long 0-$\pi$ Josephson junction consisting of 0 and $\pi$ regions having different critical current densities $j_{c,0}$ and $j_{c,\pi}$. The ground state of such a junction corresponds to a spontaneosly formed asymmetric semifluxon with tails decaying on different length scales. We calculate the depinning current of such a fractional vortex and show that it is different for positive and negative bias polarity. We also show that upon application of a bias current, the fractional flux (topological charge) associated with the vortex changes. We calculate the range of fractional flux associated with the vortex when the bias changes from negative to positive critical (depinning) values.Comment: submitted to Phys. Rev.

Advectional enhancement of eddy diffusivity under parametric disorder

Frozen parametric disorder can lead to appearance of sets of localized convective currents in an otherwise stable (quiescent) fluid layer heated from below. These currents significantly influence the transport of an admixture (or any other passive scalar) along the layer. When the molecular diffusivity of the admixture is small in comparison to the thermal one, which is quite typical in nature, disorder can enhance the effective (eddy) diffusivity by several orders of magnitude in comparison to the molecular diffusivity. In this paper we study the effect of an imposed longitudinal advection on delocalization of convective currents, both numerically and analytically; and report subsequent drastic boost of the effective diffusivity for weak advection.Comment: 14 pages, 6 figures, for Topical Issue of Physica Scripta "2nd Intl. Conf. on Turbulent Mixing and Beyond

Josephson vortex in a ratchet potential: Theory

We propose a new type of Josephson vortex ratchet. In this system a Josephson vortex moves in a periodic asymmetric potential under the action of a deterministic or random force with zero time average. For some implementations the amplitude of the potential can be controlled during the experiment, thus, allowing to tune the performance of the system and build rocking as well as flashing ratchets. We present a model describing the dynamics of the fluxon in such a system, show numerical simulation results, and discuss the differences between conventional and Josephson vortex ratchets. The investigation of this system may lead to the development of the fluxon rectifier -- a device which produces a quantized dc voltage from colored noise (non-equilibrium fluctuations).Comment: REVTeX 3.1, 9 pages, 7 figure

Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise

We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any kind of linear feedback control--single and multiple delay feedback, linear frequency filter, etc.--the phase diffusion constant, quantifying coherence, and the Lyapunov exponent, quantifying reliability, can be efficiently controlled but their ratio remains constant. Thus, an "uncertainty principle" can be formulated: the loss of reliability occurs when coherence is enhanced and, vice versa, coherence is weakened when reliability is enhanced. Treatment of this principle for ensembles of oscillators synchronized by common noise or global coupling reveals a substantial difference between the cases of slightly non-identical oscillators and identical ones with intrinsic noise.Comment: 10 pages, 5 figure

Diffusion of a passive scalar by convective flows under parametric disorder

We study transport of a weakly diffusive pollutant (a passive scalar) by thermoconvective flow in a fluid-saturated horizontal porous layer heated from below under frozen parametric disorder. In the presence of disorder (random frozen inhomogeneities of the heating or of macroscopic properties of the porous matrix), spatially localized flow patterns appear below the convective instability threshold of the system without disorder. Thermoconvective flows crucially effect the transport of a pollutant along the layer, especially when its molecular diffusion is weak. The effective (or eddy) diffusivity also allows to observe the transition from a set of localized currents to an almost everywhere intense "global" flow. We present results of numerical calculation of the effective diffusivity and discuss them in the context of localization of fluid currents and the transition to a "global" flow. Our numerical findings are in a good agreement with the analytical theory we develop for the limit of a small molecular diffusivity and sparse domains of localized currents. Though the results are obtained for a specific physical system, they are relevant for a broad variety of fluid dynamical systems.Comment: 12 pages, 4 figures, the revised version of the paper for J. Stat. Mech. (Special issue for proceedings of 5th Intl. Conf. on Unsolved Problems on Noise and Fluctuations in Physics, Biology & High Technology, Lyon (France), June 2-6, 2008

Noise Can Reduce Disorder in Chaotic Dynamics

We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or natural measure) is generally highly inhomogeneous over the set, either diminishing or enhancing the contribution of these orbits into system dynamics. We show analytically and numerically a weak noise to reduce this inhomogeneity and, additionally to obvious perturbing impact, make a regularizing influence on the chaotic dynamics. This universal effect is rooted into the nature of deterministic chaos.Comment: 11 pages, 5 figure

Model II--VV curves and figures of merit of underdamped deterministic Josephson ratchets

We propose simple models for the current-voltage characteristics of typical Josephson ratchets. We consider the case of a ratchet working against a constant applied counter force and derive analytical expressions for the key characteristics of such a ratchet: rectification curve, stopping force, input and output powers and rectification efficiency. Optimization of the ratchet performance is discussed

Phase retrapping in a pointlike φ\varphi Josephson junction: the Butterfly effect

We consider a $\varphi$ Josephson junction, which has a bistable zero-voltage state with the stationary phases $\psi=\pm\varphi$. In the non-zero voltage state the phase "moves" viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well ($-\varphi$ or $+\varphi$) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to zero-voltage state. In the limit of low damping the $\varphi$ Josephson junction exhibits a butterfly effect --- extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well

Ferromagnetic planar Josephson junction with transparent interfaces: a {\phi} junction proposal

We calculate the current phase relation of a planar Josephson junction with a ferromagnetic weak link located on top of a thin normal metal film. Following experimental observations we assume transparent superconductor-ferromagnet interfaces. This provides the best interlayer coupling and a low suppression of the superconducting correlations penetrating from the superconducting electrodes into the ferromagnetic layer. We show that this Josephson junction is a promising candidate for an experimental {\phi} junction realization.Comment: References update