Directed ratchet transport in granular chains

Directed ratchet transport of cold atoms and fluxons driven by biharmonic fields: A unified view

This paper discusses two retrodictions of the theory of ratchet universality which explain previous experimental results concerning directed ratchet transport of cold atoms in dissipative optical lattices in one case and of fluxons in uniform annular Josephson junctions in the other, both driven by biharmonic fields. It has to be emphasized that these retrodictions are in sharp contrast with the current standard explanation of such experimental results, and they offer optimal control of the ratchetlike motion of such entities. New experimental proposals with cold atoms and fluxons are discussed, providing additional tests for novel predictions from ratchet universality.

Ratchet universality in coupled dissipative oscillators without external bias

Directed ratchet transport is generally observed in nonautonomous systems as a result of the interplay of nonlinearity, symmetry breaking, and nonequilibrium fluctuations. Here we demonstrate that ratchet dynamics can appear in significant transporting degrees of freedom of dissipative coupled systems without external bias due to unidirectional coupling of oscillatory degrees of freedom (which are also nonbiasing in any direction), while optimal enhancement of directed ratchet transport occurs when the initial conditions and parameters of such ratcheting degrees of freedom are suitably chosen as predicted by the theory of ratchet universality. The simple case of linear oscillatory degrees of freedom is discussed in detail, and numerical experiments are described which confirm all the theoretical predictions, including the dependence of current (velocity) reversals on the initial conditions and the ratcheting degrees-of-freedom parameters. This autonomous ratchet scenario could be exploited technologically, for instance, in the context of noncontact, rack-and-pinion type, nanoscale setups with coupling from the lateral Casimir force, and is relevant for studies of molecular motors in the biological realm.

Ratchet universality in the bidirectional escape from a symmetric potential well

The present work discusses symmetry-breaking-induced bidirectional escape from a symmetric metastable potential well by the application of zero-average periodic forces in the presence of dissipation. We characterized the interplay between heteroclinic instabilities leading to chaotic escape and breaking of a generalized parity symmetry leading to directed ratchet escape to an attractor either at ∞ or at -∞. Optimal enhancement of directed ratchet escape is found to occur when the wave form of the zero-average periodic force acting on the damped driven oscillator matches as closely as possible to a universal wave form, as predicted by the theory of ratchet universality. Specifically, the optimal approximation to the universal force triggers the almost complete destruction of the nonescaping basin for driving amplitudes which are systematically lower than those corresponding to a symmetric periodic force having the same period. We expect that this work could be potentially useful in the control of elementary dynamic processes characterized by multidirectional escape from a potential well, such as forced chaotic scattering and laser-induced dissociation of molecular systems, among others.

Soliton ratchet induced by random transitions among symmetric sine-Gordon potentials

The generation of net soliton motion induced by random transitions among N symmetric phase-shifted sine-Gordon potentials is investigated, in the absence of any external force and without any thermal noise. The phase shifts of the potentials and the damping coefficients depend on a stationary Markov process. Necessary conditions for the existence of transport are obtained by an exhaustive study of the symmetries of the stochastic system and of the soliton velocity. It is shown that transport is generated by unequal transfer rates among the phase-shifted potentials or by unequal friction coefficients or by a properly devised combination of potentials (N>2). Net motion and inversions of the currents, predicted by the symmetry analysis, are observed in simulations as well as in the solutions of a collective coordinate theory. A model with high efficient soliton motion is designed by using multistate phase-shifted potentials and by breaking the symmetries with unequal transfer rates.

Directed motion of spheres induced by unbiased driving forces in viscous fluids beyond the Stokes' law regime

The emergence of directed motion is investigated in a system consisting of a sphere immersed in a viscous fluid and subjected to time-periodic forces of zero average. The directed motion arises from the combined action of a nonlinear drag force and the applied driving forces, in the absence of any periodic substrate potential. Necessary conditions for the existence of such directed motion are obtained and an analytical expression for the average terminal velocity is derived within the adiabatic approximation. Special attention is paid to the case of two mutually perpendicular forces with sinusoidal time dependence, one with twice the period of the other. It is shown that, although neither of these two forces induces directed motion when acting separately, when added together, the resultant force generates directed motion along the direction of the force with the shortest period. The dependence of the average terminal velocity on the system parameters is analyzed numerically and compared with that obtained using the adiabatic approximation. Among other results, it is found that, for appropriate parameter values, the direction of the average terminal velocity can be reversed by varying the forcing strength. Furthermore, certain aspects of the observed phenomenology are explained by means of symmetry arguments.

Spectroscopy and Directed Transport of Topological Solitons in Crystals of Trapped Ions

We study experimentally and theoretically discrete solitons in crystalline structures consisting of several tens of laser-cooled ions confined in a radio frequency trap. Resonantly exciting localized, spectrally gapped vibrational modes of the soliton, a nonlinear mechanism leads to a nonequilibrium steady state of the continuously cooled crystal. We find that the propagation and the escape of the soliton out of its quasi-one-dimensional channel can be described as a thermal activation mechanism. We control the effective temperature of the soliton's collective coordinate by the amplitude of the external excitation. Furthermore, the global trapping potential permits controlling the soliton dynamics and realizing directed transport depending on its topological charge.

Kink ratchet induced by a time-dependent symmetric field potential

The ratchet effect of a sine-Gordon kink is investigated in the absence of any external force while the symmetry of the field potential at every time instant is maintained. The directed motion appears by a time shift of the sine-Gordon potential through a time-dependent additional phase. A symmetry analysis provides the necessary conditions for the existence of net motion. It is also shown analytically, by using a collective coordinate theory, that the novel physical mechanism responsible for the appearance of the ratchet effect is the coupled dynamics of the kink width with the background field. Biharmonic and dichotomic periodic variations of the additional phase of the sine-Gordon potential are considered. The predictions established by the symmetry analysis and the collective coordinate theory are verified by means of numerical simulations. Inversion and maximization of the resulting current as a function of the system parameters are investigated.

Horizontal flow and surface patterns in a vertically vibrated annular granular layer

A set of experiments was carried out on the motion of granular materials in a vertically vibrated annular system with a sawtooth-shaped base. We observed the coexistence of granular flow and surface patterns such as periodic subharmonic waves and kink pairs. Different patterns can transit each other as control parameters vary. The flow varies with space and time, and oppositely directed flows can occur at different levels and different moments. The magnitude and direction of the flow depend on the parameters defining the system in a complex manner. The motion of the patterns relates to the granular flow in a different way from that in which the wave in an ordinary fluid relates to the moving fluid. A preliminary explanation is given to our experimental findings.

Quantum parameter space of dissipative directed transport

Quantum manifestations of isoperiodic stable structures (QISSs) have a crucial role in the current behavior of quantum dissipative ratchets. In this context, the simple shape of the ISSs has been conjectured to be an almost exclusive feature of the classical system. This has drastic consequences for many properties of the directed currents, the most important one being that it imposes a significant reduction in their maximum values, thus affecting the attainable efficiency at the quantum level. In this work we prove this conjecture by means of comprehensive numerical explorations and statistical analysis of the quantum states. We are able to describe the quantum parameter space of a paradigmatic system for different values of ℏ(eff) in great detail. Moreover, thanks to this we provide evidence on a mechanism that we call parametric tunneling by which the sharp classical borders of the regions in parameter space become blurred in the quantum counterpart. We expect this to be a common property of generic dissipative quantum systems.