Jamming and diode effects for vortices in nanostructured superconductors

We examine jamming and ratchet effects for vortex matter in superconductors with asymmetric funnel geometries. We show that the vortex–vortex interactions can induce a clogging or jamming effect where it becomes increasingly difficult for the vortices to move through the system. We also find that commensurability effects can arise when certain vortex configurations form highly symmetrical structures in the funnel plaquettes. Due to the asymmetry, the critical currents are different for driving in different directions, leading to a diode effect. We also discuss other possible geometries and approaches that could be used to explore jamming in vortex matter, such as an analog to a granular hopper and a single driven vortex probe moving through an array of other vortices.     

Ratchet cellular automata

In this work we propose a ratchet effect which provides a general means of performing clocked logic operations on discrete particles, such as single electrons or vortices. The states are propagated through the device by the use of an applied ac drive. We numerically demonstrate that a complete logic architecture is realizable using this ratchet. We consider specific nanostructured superconducting geometries using superconducting materials under an applied magnetic field, with the positions of the individual vortices in samples acting as the logic states. These devices can be used as the building blocks for an alternative microelectronic architecture.     

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.     

Magnetic ratchet effects in a two-dimensional electron gas

The effect of the magnetic field on the generation of an electric current in a two-dimensional electronic ratchet is theoretically studied. Mechanisms of the formation of magnetically induced photocurrent are proposed for a structure with a two-dimensional electron gas (quantum well, graphene, or topological insulator) with a lateral asymmetric superlattice consisting of metallic strips on the external surface of the structure. The ratchet with the spatially oscillating magnetic field generated by the ferromagnetic lattice, as well as the nonmagnetic ratchet placed in the uniform magnetic field both classically weak and strong quantizing, is considered. It is established that the ratio of the amplitude of the magnetic oscillations of photocurrent to the ratchet photocurrent in zero field can exceed two orders of magnitude.     

Fixation of advantageous mutations in an off-equilibrium population

We investigate the evolution of asexual populations subject to a large supply of deleterious mutations such that Muller's ratchet operates. In this regime, the accumulation of deleterious mutations takes place continuously with the resulting loss of the least-loaded class of individuals. In the current work, we study the effect of the supply of beneficial mutations on the ratchet's speed. We also examine how the rate of substitution of favorable mutations as well as the mean selective effect of favorable mutations that reach fixation is compared to those assuming a population at equilibrium. We observe that under Muller's ratchet, the rate of fixation of advantageous mutations is higher than that predicted for an equilibrium population. The difference between the rate supposing an equilibrium regime and that for the non-equilibrium case becomes larger as we increase the rate of deleterious mutations. On the other hand, the mean selective effect of beneficial mutations that reach fixation is smaller than the expected value for the equilibrium situation.     

Current-driven dynamics in Josephson junction networks with an asymmetric potential

Current-driven dynamics of Josephson junction networks (JJNs) is studied using numerical simulations. We consider a JJN with an asymmetric and periodic potential of vortices, which is realized by saw-tooth modulation of junction critical currents. When external ac currents are applied to the JJN in a magnetic field, there appears a ratchet effect, and then directed motion of vortices is induced in certain system parameter regimes. A ratchet behavior is observed even for JJNs with weak structural disorder. We clarify the vortex pinning and dynamics in the JJN as a ratchet system.     

Rectification in Luttinger liquids

We investigate the rectification of an ac bias in Luttinger liquids in the presence of an asymmetric potential (the ratchet effect). We show that a strong repulsive electron interaction enhances the ratchet current in comparison with Fermi-liquid systems, and the dc I-V curve is strongly asymmetric in the low-voltage regime even for a weak asymmetric potential. At higher voltages the ratchet current exhibits an oscillatory voltage dependence.     

Mutation accumulation in growing asexual lineages

The stochastic loss of entire classes of individuals bearing the fewest number of mutations-a process known as Muller's ratchet-is studied in asexual populations growing unconstrained from a single founder. In the neutral regime, where mutations have zero effect on fitness, we derive a recursion equation for the probability distribution of the minimum number of mutations carried by individuals in the least-loaded class, and obtain an explicit condition for the halting of the ratchet. Next, we consider the case of deleterious mutations, and show that weak selection can actually accelerate the ratchet beyond that achieved for the neutral regime. This effect is transitory, however, as our results suggest that even weak purifying selection will eventually lead to the complete cessation of the ratchet. These results may have important implications for problems in biology and the medical sciences.     

Drift ratchet

We consider a silicon wafer, pierced by millions of identical pores with periodically varying diameters but without spatial inversion symmetry (ratchet profile). When a liquid is periodically pumped back and forth through the pores, our theory predicts a net transport of suspended micrometer-sized particles (drift ratchet). The direction of this particle current depends very sensitively on the size of the particles. For typical parameter values of the experiment, two different types of particles at an initially homogeneous 1:1 mixture are spatially separated with a purity beyond 1:1000 on a time scale of a few hours in comparably large quantities. This result is due to the highly parallel architecture of the device. The experimental realization of the setup, presently under construction, thus appears to be a promising new particle separation device, possibly superior to existing methods for particles sizes on the micrometer scale.     

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     

Quantitative simulations of ratchet potential in a dusty plasma ratchet

Using a dusty plasma ratchet, one can realize the rectification of charged dust particle in a plasma. To obtain the ratchet potential dominating the rectification, here we perform quantitative simulations based on a two-dimensional fluid model of capacitively coupled plasma. Plasma parameters are firstly calculated in two typical cross sections of the dusty plasma ratchet which cut vertically the saw channel at different azimuthal positions. The balance positions of charged dust particle in the two cross sections then can be found exactly. The electric potentials at the two balance positions have different values. Using interpolation in term of a double-sine function from previous experimental measurement, an asymmetrical ratchet potential along the saw channel is finally obtained. The asymmetrical orientation of the ratchet potential depends on discharge conditions. Quantitative simulations further reproduce our previous experimental phenomena such as the rectification of dust particle in the dusty plasma ratchet.     

Stationary probability flow and vortices for the Smoluchowski–Feynman ratchet

Smoluchowski–Feynman ratchet is in contact with two heat reservoirs with different temperatures. We study the non-equilibrium stationary state with a ratchet rotating unidirectionally, based on the probability flow field, which are obtained either by solving the Fokker–Planck equation (with no inertial effect) or by computer simulations (with an inertial effect). Vortex pattern in the probability flow is found, whose sense of rotation, on the one hand, is determined by a simple thermodynamic argument and, on the other hand, determines rotational direction of the ratchet. Small efficiency of the ratchet is also discussed within this vortex framework.     

Photonic ratchet superlattices by optical multiplexing

We present a method based on incremental holographic multiplexing to create a refractive index ratchet distribution into a photorefractive crystal as an example for the generation principle of such complex multiperiodic lattices. The implemented technique follows a finite optical series expansion of the desired index modulation. To analyze the induced lattice, we determine the phase retardation of a probe beam at the back face of the crystal by digital holography analysis. Our result depicts a first example to optically explore the fascinating phenomena of ratchet resembling systems.     

Active Brownian motion models and applications to ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.     

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     

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.     

Chaotic Ratchet Effect for Bose-Einstein Condensed Atoms in 1D Optical Lattices

The chaotic ratchet effect for Bose-Einstein condensed atoms in an optical lattice is investigated. By using the direct perturbation method we obtain the chaotic solution of the condensed system. Theoretical analysis reveals that the transport of the condensed atoms in the ratchet potential is a chaotic one, and corresponding numerical results agree well with the theoretical results.     

空时非对称分数阶类Langevin棘齿

研究了空时非对称分数阶类Langevin分子马达棘齿模型,其中势函数是空间对称破缺的周期势,时间非对称类Langevin噪声由Logistic映射生成,而分数阶则刻画了分子马达工作环境的非理想程度.通过将模型转化为离散映射,即研究其整时间点情形,数值模拟了噪声的时间非对称性、势函数的空间非对称性以及分数阶对模型定向输运行为的影响.数值模拟结果表明:噪声的时间非对称性是定向流产生的根源,而势函数的空间非对称性能够与其进行竞争与协作,并在适当的参数条件下导致定向流的逆转;分数阶仅影响定向流的大小而不改变其方向.与经典的整数阶分子马达模型或时间非对称分数阶分子马达棘齿模型相比,该模型可以更为真实地描述分子马达的噪声整流工作机理.     

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.     

Relativistic graphene ratchet on semidisk Galton board

Using extensive Monte Carlo simulations we study numerically and analytically a photogalvanic effect, or ratchet, of directed electron transport induced by a microwave radiation on a semidisk Galton board of antidots in graphene. A comparison between usual two-dimensional electron gas (2DEG) and electrons in graphene shows that ratchet currents are comparable at very low temperatures. However, a large mean free path in graphene should allow to have a strong ratchet transport at room temperatures. Also in graphene the ratchet transport emerges even for unpolarized radiation. These properties open promising possibilities for room temperature graphene based sensitive photogalvanic detectors of microwave and terahertz radiation.