Bifurcations and sudden current change in ensembles of classically chaotic ratchets

Absolute negative mobility induced by potential phase modulation

We investigate the transport properties of a particle subjected to a deterministic inertial rocking system, under a constant bias, for which the phase of the symmetric spatial potential used is time modulated. We show that this modulated phase, assisted by a periodic driving force, can lead to the occurrence of the so-called absolute negative mobility (ANM), the phenomenon in which the particle surprisingly moves against the bias. Furthermore, we discover that ANM predominantly originates from chaotic-periodic transitions. While a detailed mechanism of ANM remains unclear, we show that one can manipulate the control parameters, i.e., the amplitude and the frequency of the phase, in order to enforce the motion of the particle in a given direction. Finally, for this experimentally realizable system, we devise a two-parameter current plot which may be a good guide for controlling ANM.

Persistence of uphill anomalous transport in inhomogeneous media

For systems out of equilibrium and subjected to a static bias force it can often be expected that particle transport will usually follow the direction of this bias. However, counterexamples exist where particles exhibit uphill motion (known as absolute negative mobility, ANM), particularly in the case of coupled particles. Examples in single particle deterministic systems are less common. Recently, in one such example, uphill motion was shown to occur for an inertial driven and damped particle in a spatially symmetric periodic potential. The source of this anomalous transport was a combination of two periodic driving signals which together are asymmetric under time reversal. In this paper we investigate the phenomena of ANM for a deterministic particle evolving in a periodic and symmetric potential subjected to an external unbiased periodic driving and nonuniform space-dependent damping. It will be shown that this system exhibits a complicated response behavior as certain control parameters are varied, most notably being enhanced parameter regimes exhibiting ANM as the static bias force is increased. Moreover, the solutions exhibiting ANM are shown to be, at least over intermediate time periods, superdiffusive, in contrast to the solutions that follow the bias where the diffusion is normal.

Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment

We investigate the collective dynamics of a network of inertia particles diffusing in a ratchet potential and interacting indirectly through their stochastic dynamical environment. We obtain analytically the condition for the existence of a stable collective state, and we show that the number N of particles in the network, and the strength k of their interaction with the environment, play key roles in synchronization and transport processes. Synchronization is preceded by symmetry-breaking associated with double-resonance oscillations and is shown to be strongly dependent on the network size: convergence to the synchronization manifold occurs much faster with a large network. For small networks, increasing the noise level enhances synchronization in the weakly coupled regime, while particles in a large network are weakly synchronized. Similarly, in the strongly coupled regime, particles in a small network are weakly synchronized; whereas the synchronization is strong and robust against noise when the network-size is large. Small and moderate networks maximize and stabilize efficient transport. Although the dynamics for larger networks is highly correlated, the transport current is erratic.

Effects of phase disorder on transport of globally coupled Brownian motors

The transport of N globally coupled Brownian motors driven by a periodic force with phase disorder is investigated. An approximate theoretical analysis of the model is presented. The effects of the phase disorder and the driving strength of the periodic force on the transport of the coupled Brownian motors are discussed both theoretically and numerically. It is found that the increase of the periodical driving force decreases the average velocity, while the coupled particles may benefit from the phase disorder to enhance collective transport.

Current reversals in a rocking ratchet: the frequency domain

Motivated by recent work [D. Cubero et al., Phys. Rev. E 82, 041116 (2010)], we examine the mechanisms which determine current reversals in rocking ratchets as observed when varying the frequency of the drive. We found that a class of these current reversals in the frequency domain is precisely determined by dissipation-induced symmetry breaking. Our experimental and theoretical work thus extends and generalizes the previously identified relationship between dynamical and symmetry-breaking mechanisms in the generation of current reversals.

Current reversals and synchronization in coupled ratchets

Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on ratchet mechanism. By considering a system of two interacting ratchets, we demonstrate how the coupling can be used to control the reversals. In particular, we find that current reversal that exists in a single driven ratchet system can ultimately be eliminated with the presence of a second ratchet. For specific coupling strengths a current-reversal free regime has been detected. Furthermore, in the fully synchronized state characterized by the coupling threshold k(th), a specific driving amplitude a(opt) is found for which the transport is optimum.

Noise-induced multi-decrease and multi-increase of net voltage in Josephson junctions

In this paper, we investigate the net voltage in the Josephson junction subject to a thermal noise, a dc constant bias electric current and an ac time-periodic electric drive for the overdamped case and underdamped case simultaneously. It is shown that, by increasing the thermal noise strength, the net voltage can be decreased and increased several times as a function of the driving frequency. In addition, noise-enhanced stability is found for the net voltage of the junction.

Directed transport in periodically rocked random sawtooth potentials

We study directed transport of overdamped particles in a periodically rocked random sawtooth potential. Two transport regimes can be identified which are characterized by a nonzero value of the average velocity of particles and a zero value, respectively. The properties of directed transport in these regimes are investigated both analytically and numerically in terms of a random sawtooth potential and a periodically varying driving force. Precise conditions for the occurrence of transition between these two transport regimes are derived and analyzed in detail.

Transport control in a deterministic ratchet system

We study the control of transport properties in a deterministic inertia ratchet system via the extended delay feedback method. A chaotic current of a deterministic inertia ratchet system is controlled to a regular current by stabilizing unstable periodic orbits embedded in a chaotic attractor of the unperturbed system. By selecting an unstable periodic orbit, which has a desired transport property, and stabilizing it via the extended delay feedback method, we can control transport properties of the deterministic inertia ratchet system. Also, we show that the extended delay feedback method can be utilized for separation of particles in the deterministic inertia ratchet system as a particle's initial condition varies.

Controlling the ratchet effect for cold atoms

Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.

Ratchet effect and the transporting islands in the chaotic sea

We study directed transport in a classical deterministic dissipative system. We consider the generic case of mixed phase space and show that large ratchet currents can be generated thanks to the presence, in the Hamiltonian limit, of transporting stability islands embedded in the chaotic sea. Because of the simultaneous presence of chaos and dissipation the stationary value of the current is independent of initial conditions, except for initial states with very small measure.