Two particles with bistable coupling on a ratchet

We study the motion of two Brownian particles coupled by a bistable potential on a periodically rocked ratchet. Bistable coupling symmetrizes the two particles and admits a richer dynamics that cannot be found with linear coupling or a single particle. Depending on the coupling strength and the equilibrium distance we find different step patterns and current reversals. We present numerical results and compare them with analytical solutions in limiting cases of adiabatically slow rocking and of rigid coupling.     

Entropy in quantum ratchet for a delta-kicked model

We investigate the evolution of Shannon entropy in quantum ratchet effect for a delta-kicked model, where a particle with initial momentum zero is periodically kicked by an asymmetric potential. It is shown that the evolution of Shannon entropy of the particle can remarkably reflect whether quantum resonance emerges and gives rise to ratchet current or not. Furthermore, for different kinds of quantum resonances, low-order or high-order quantum resonances, the evolutions of the entropy are quite different.     

Dynamics of Particles Trapped by Dissipative Domain Walls

We study the interactions of the dissipative domain walls with dielectric particles. It is shown that particles can be steadily trapped by the moving domain walls. The influence of the ratchet effect on particle trapping is considered. It is demonstrated, that the ratchet effect allows to obtain high accuracy in particle manipulation.

     

Controlling the motion of interacting particles: homogeneous systems and binary mixtures

We elaborate on recent results on the transport of interacting particles for both single-species and binary mixtures subject to an external driving on a ratchetlike asymmetric substrate. Moreover, we also briefly review motion control without any spatial asymmetric potential (i.e., no ratchet). Our results are obtained using an analytical approach based on a nonlinear Fokker-Planck equation as well as via numerical simulations. By increasing the particle density, the net dc ratchet current in our alternating (ac)-driven systems can either increase or decrease depending on the temperature, the drive amplitude, and the nature of the inter-particle interactions. This provides an effective control of particle motion by just changing the particle density. At low temperatures, attracting particles can condense at some potential minima, thus breaking the discrete translational symmetry of the substrate. Depending on the drive amplitude, an agglomeration or condensation results either in a drop to zero or in a saturation of the net particle velocity at densities above the condensation density-the latter case producing a very efficient rectification mechanism. For binary mixtures we find three ways of controlling the particle motion of one (passive) B species by means of another (active) A species: (i) Dragging the target particles B by driving the auxiliary particles A, (ii) rectifying the motion of the B particles on the asymmetric potential created by the A-B interactions, and (iii) dynamically modifying (pulsating) this potential by controlling the motion of the A particles. This allows to easily control the magnitude and direction of the velocity of the target particles by changing either the frequency, phase and/or amplitude of the applied ac drive(s).     

SQUID ratchets: basics and experiments

Superconducting quantum interference devices (SQUIDs) are very well suited for experimental investigations of ratchet effects. This is due to the periodicity of the Josephson coupling energy with respect to the phase difference δ of the superconducting macroscopic wave function across a Josephson junction. We show first that, within the resistively and capacitively shunted junction model, the equation of motion for δ is equivalent to the motion of a particle in the so-called tilted washboard potential, and we derive the conditions which have to be satisfied to build a ratchet potential based on asymmetric dc SQUIDs. We then present results from numerical simulations and experimental investigations of dc SQUID ratchets with critical-current asymmetry under harmonic excitation (periodically rocking ratchets). We discuss the impact of important properties like damping or thermal noise on the operation of SQUID ratchets in various regimes, such as adiabatically slow or fast nonadiabatic excitation. Received: 22 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Brownian motors and stochastic resonance

We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.     

Feedback control in a collective flashing ratchet

An ensemble of Brownian particles in a feedback controlled flashing ratchet is studied. The ratchet potential is switched on and off depending on the position of the particles, with the aim of maximizing the current. We study in detail a protocol which maximizes the instant velocity of the center of mass of the ensemble at any time. This protocol is optimal for one particle and performs better than any periodic flashing for ensembles of moderate size, but is defeated by a random or periodic switching for large ensembles.     

Investigation on a temporal asymmetric oscillating temperature ratchet

We study the directed motion of Brownian particles in a periodic potential due to a periodically oscillating temperature of the thermal environment. The steady average velocity of Brownian particles is evaluated by using the Langevin simulation. The features of current are discussed in detail. The results obtained here show that the periodically oscillating temperature produces a directed transport of the particles in a ratchet system and that through changing some parameters of this system, the magnitude and direction of transport can be controlled. Moreover, it is found that the temporal symmetric temperature oscillation may not be the best choice and the mode of temperature oscillation can be optimized.     

Deterministic inhomogeneous inertia ratchets

We study the deterministic dynamics of a periodically driven particle in the underdamped case in a spatially symmetric periodic potential. The system is subjected to a space-dependent friction coefficient, which is similarly periodic as the potential but with a phase difference. We observe that frictional inhomogeneity in a symmetric periodic potential mimics most of the qualitative features of deterministic dynamics in a homogeneous system with an asymmetric periodic potential. We point out the need of averaging over the initial phase of the external drive at small frictional inhomogeneity parameter values or analogously low potential asymmetry regimes in obtaining ratchet current. We also show that at low amplitudes of the drive, where ratchet current is not possible in the deterministic case, noise plays a significant role in realizing ratchet current.     

A Brownian-ratchet DNA pump with applications to single-nucleotide polymorphism genotyping

We have fabricated a micron-scale device capable of transporting DNA oligomers using Brownian ratchets. The ratchet potential is generated by applying a voltage difference to interdigitated electrodes. Cycling between the charged state and a discharged, free-diffusion state rectifies the Brownian motion of charged particles. The observed macroscopic transport properties agree with the transport rate predicted from microscopic parameters including the DNA diffusivity, the dimensions of the ratchet potential, and the cycling time. Applications to human genetics, primarily genotyping of single-nucleotide polymorphisms (SNPs), are discussed. Received: 7 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Control-oriented approaches to anticipating synchronization of chaotic deterministic ratchets

In virtue of techniques derived from nonlinear control system theory, we establish conditions under which one could obtain anticipating synchronization between two periodically driven deterministic ratchets that are able to exhibit directed transport with a finite velocity. Criteria are established in order to guarantee the anticipating synchronization property of such systems as well as characterize phase space dynamics of the ratchet transporting behaviors. These results allow one to predict the chaotic direct transport features of particles on a ratchet potential using a copy of the same system that performs as a slave, which are verified through numerical simulation.     

Quantum ratchets and quantum heat pumps

Quantum ratchets are Brownian motors in which the quantum dynamics of particles induces qualitatively new behavior. We review a series of experiments in which asymmetric semiconductor devices of sub-micron dimensions are used to study quantum ratchets for electrons. In rocked quantum-dot ratchets electron-wave interference is used to create a non-linear voltage response, leading to a ratchet effect. The direction of the net ratchet current in this type of device can be sensitively controlled by changing one of the following experimental variables: a small external magnetic field, the amplitude of the rocking force, or the Fermi energy. We also describe a tunneling ratchet in which the current direction depends on temperature. In our discussion of the tunneling ratchet we distinguish between three contributions to the non-linear current–voltage characteristics that lead to the ratchet effect: thermal excitation over energy barriers, tunneling through barriers, and wave reflection from barriers. Finally, we discuss the operation of adiabatically rocked tunneling ratchets as heat pumps. Received: 8 February 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Rectification Efficiency of Two Harmonically Coupled Particles

Transportation properties of two harmonically coupled particles moving in a flashing or rocking ratchet potential are investigated in terms of Langevin simulation. The efficiency for rectification of non-equilibrium fluctuation is calculated by using a new definition. The results show that both the average current and efficiency of two coupled particles in the flashing ratchet are larger than that of a single particle and these quantities are non-monotonous functions of the potential remaining time.     

外力作用下反馈耦合布朗棘轮的定向输运

本文研究了处于外力作用下双阱棘轮势中两个反馈耦合布朗粒子的定向输运性能. 通过对过阻尼朗之万方程的数值求解, 详细讨论了外力、热噪声与势阱的不对称参数等对耦合布朗粒子的平均速度、 有效扩散系数及Pe数的影响. 研究发现, 平均速度随外力呈周期性的变化规律. 同时耦合系统存在最优噪声强度会使定向输运达到最强. 值得指出的是棘轮系统可通过改变双阱势的结构来获得较强的定向流. 关键词： 耦合布朗棘轮 外力 双阱棘轮势 平均速度     

周期驱动玻色-爱因斯坦凝聚系统的棘齿效应

研究了周期脉冲驱动下的玻色-爱因斯坦凝聚体系（BEC）的动力学演化.其中着重考虑了BEC原子间的非线性相互作用对量子棘齿效应的影响.数值计算结果表明,较弱的非线性相互作用可以减弱定向动量流的强度.而较强的非线性相互作用则会使量子棘齿效应消失甚至发生反转,即系统会出现反向的定向动量流,而且随着时间的演化,动量流会表现出微弱的饱和趋势.计算还发现,高阶量子共振下系统的棘齿效应变得很不明显,而且外部驱动势的周期噪声很容易破坏体系的棘齿效应. 关键词： 玻色-爱因斯坦凝聚 量子混沌 量子共振 棘齿效应     

Directed transport of coupled Brownian ratchets with time-delayed feedback

A time-delayed feedback ratchet consisting of two Brownian particles interacting through the elastic spring is consid ered. The model describes the directed transport of coupled Brownian particles in an asymmetric two-well ratchet potential which can be calculated theoretically and implemented experimentally. We explore how the centre-of-mass velocity is af fected by the time delay, natural length of the spring, amplitude strength, angular frequency, external force, and the structure of the potential. It is found that the enhancement of the current can be obtained by varying the coupling strength of the delayed feedback system. When the thermal fluctuation and the harmonic potential match appropriately, directed current evolves periodically with the natural length of the spring and can achieve a higher transport coherence. Moreover, the external force and the amplitude strength can enhance the directed transport of coupled Brownian particles under certain conditions. It is expected that the polymer of large biological molecules may demonstrate a variety of novel cooperative effects in real propelling devices.     

Efficiency of particle charging by an alternating electric field charger

Alternating electric field charger is a device in which the particles are charged by ionic current and periodically deflected by alternating electric field during their flow through the charger. The oscillatory motion of small amplitude reduces the particle loss within the charger. The results of measurements of mean charge of the particles at the outlet and their penetration through the charger are presented in the paper.     

Transport and dynamical properties of inertial ratchets

In this paper we discuss the dynamics and transport properties of a massive particle in a ratchet type potential immersed in a dissipative environment. The directional currents and characteristics of the motion are studied as the specific frictional coefficient varies, finding that the stationary regime is strongly dependent on this parameter. The maximal Lyapunov exponent and the current show large fluctuations and inversions, therefore for some range of the control parameter, this inertial ratchet could originate a mass separation device. Also an exploration of the effect of a random force on the system is performed.