Periodic Ratchet Potential Research Articles

Brownian dynamics of Dirac fermions in twisted bilayer graphene

Brownian dynamics of Dirac fermions in twisted bilayer graphene is investigated within the framework of semiclassical relativistic Langevin equations. We find that under the influence of orthogonal, commensurate ac drives in the periodic ratchet potential of a substrate, the charge carriers in the system exhibit pronounced random dynamics, tuned by the twist angle, making twisted bilayer graphene distinct from monolayer graphene. It is shown that as threshold twist angle matches the optimal angle, deterministic running states appear in the limit of weak thermal noise where the diffusion rate is enhanced significantly compared to bare thermal diffusion. Analysis of the real space trajectories and diffusion coefficient illustrates the significant role of thermal noise in the random motion of Dirac fermions. In addition, we find that the Brownian particle shows remarkable ratchet effect as a net current.

Aging in the transport on the corrugated ratchet potential

Under rapid undercooling, glass forming liquids freeze in an amorphous state that can equilibrate only on enormously long time-scales, This is the characteristic sign of aging, which has been observed in a wide range of systems. Brownian ratchet is a widely studied system that exhibits many types of anomalous dynamical behavior. We have investigated the possibility of aging in the collective motion of Brownian particles in a periodic ratchet potential with quenched disorder. We find that when a slowly growing fraction of particles are trapped for long time, the collective movement tends to become super-diffusive. The super-diffusive transport weakly breaks the ergodicity and the time to cover the whole phase space become enormously long and reminiscent of aging behavior.

Coherent motion of vortices driven by alternating currents in an annular Josephson ratchet ladder

Vortex dynamics have been investigated numerically in a double-ring annular ladder composed of Josephson ratchet network along the circular direction. One repeat unit of the periodic ratchet potential consists of two adjacent plaquettes of different sizes, where the critical currents of their rung junctions are also assigned with different values. Each vortex generated between the two rings by a transverse magnetic field oscillates through several plaquettes or rotates along the ladder, depending on the magnitude of direct and alternating currents applied to the radial direction. Because of the broken spatial symmetry in the potential landscape, onsets of the vortex motion and widths of the Shapiro steps in the current-voltage characteristics show polarity-dependent behavior. The directional motion of vortices, already known in rectangular Josephson ratchet networks driven by alternating currents, has also been confirmed to appear as directional rotation in this annular ratchet ladder. A notable feature is that such dynamics can occur with a system’s commensurate condition that makes a Shapiro step at zero direct current, which leads to coherent rotational motion of vortices. Here, we report that for each magnetic flux applied to the system there is a finite range of alternating currents that allow vortices to move coherently.

Irreversible Brownian Heat Engine

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine $$\eta =1-\sqrt{{T_{c}/T_{h}}}$$ [23]. On the other hand, the maximum power efficiency of the engine approaches $$\eta ^{MAX}=1-({T_{c}/T_{h}})^{1\over 4}$$ . It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.

Vortex dynamics in an annular Josephson ratchet ladder

We present numerically the motion of vortices placed in an annular Josephson ladder which has a periodic ratchet potential along the annular direction. The ratchet characteristics are provided by assigning both alternate critical currents and alternate plaquette areas. The vortices are subject to an external current applied uniformly from each superconducting grain in the inner ring to each grain in the outer ring. The current-voltage (I-V) curves show asymmetric features because of the spatially broken symmetry of the potential. When an alternating current is added to the external current, Shapiro steps appear in the I-V curves, showing asymmetric values of the step widths and on-set currents. For a certain range of the alternating currents, vortices rotate to the easy direction, even at zero driving current, that corresponds to the direction away from the steep slope and toward the gentle slope of the ratchet potential.

The effect of temperature dependence of viscosity on a Brownian heat engine

We modeled a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a spatially varying temperature. The strength for the viscous friction γ(x) is considered to decrease exponentially when the temperature T(x) of the medium increases (γ(x) = Be− AT(x)) as proposed originally by Reynolds [O. Reynolds, Phil. Trans. R. Soc. London 177, 157 (1886)]. Our result depicts that the velocity of the motor is considerably higher when the viscous friction is temperature dependent than that of the case where the viscous friction is temperature independent. The dependence of the efficiency η as well as the coefficient of performance of the refrigerator Pref on model parameters is also explored. If the motor designed to achieve a high velocity against a frictional drag, in the absence of external load f, we show that Carnot efficiency or Carnot refrigerator is unattainable even at quasistatic limit as long as the viscous friction is temperature dependent A ≠ 0. On the contrary, in the limit A → 0 or in general in the presence of an external load (for any A) f ≠ 0, at quasistatic limit, Carnot efficiency or Carnot refrigerator is attainable as long as the heat exchange via kinetic energy is omitted. For all cases, far from quasistatic limit, the efficiency and the coefficient of performance of the refrigerator are higher for constant γ case than the case where γ is temperature dependent. On the other hand, if one includes the heat exchange at the boundary of the heat baths, Carnot efficiency or Carnot refrigerator is unattainable even at quasistatic limit. Moreover, the dependence for the optimized and maximum power efficiencies on the determinant model parameters is explored.

A two-dimensional coupled directed transport model

Under the effect of external driving force and noise, a directed transport model for coupled particles in a two-dimensional potential is established. Here, a one-dimensional potential is taken as the periodic piecewise ratchet potential, and the other one is taken as the periodic symmetric non-ratchet potential to which the external periodic driving force and noise are applied. According to the nonequilibrium statistical theory and the nonlinear dynamics, the transport characters of the coupled system in the overdamped case are researched and discussed. Numerical results show that an obvious directed transport can appear both in the ratchet potential and in the non-ratchet potential case. But, the average velocities of the coupled system in the two potentials have completely different dependence on the system parameters. In the case of ratchet potential, the average velocity is strongly dependent on the coupling intensity, noise intensity, the driving strength, and the particle population; the average velocity can reach the maximum at appropriate coupling intensity, noise intensity, the driving strength or the particle population. Otherwise, in the case of non-ratchet potential, the average velocity is strongly dependent on the barrier height for the non-ratchet potential, but fluctuates as the coupling intensity, the driving strength, the driving initial phase difference or the particle population varies. This shows that the average velocity of the coupled system in the non-ratchet potential has weak dependence on system parameters, including the coupling intensity, the driving strength, the driving initial phase difference and the particle population.

Subdiffusive rocking ratchets in viscoelastic media: Transport optimization and thermodynamic efficiency in overdamped regime

We study subdiffusive overdamped Brownian ratchets periodically rocked by an external zero-mean force in viscoelastic media within the framework of a non-Markovian generalized Langevin equation approach and associated multidimensional Markovian embedding dynamics. Viscoelastic deformations of the medium caused by the transport particle are modeled by a set of auxiliary Brownian quasiparticles elastically coupled to the transport particle and characterized by a hierarchy of relaxation times which obey a fractal scaling. The most slowly relaxing deformations which cannot immediately follow to the moving particle imprint long-range memory about its previous positions and cause subdiffusion and anomalous transport on a sufficiently long time scale. This anomalous behavior is combined with normal diffusion and transport on an initial time scale of overdamped motion. Anomalously slow directed transport in a periodic ratchet potential with broken space inversion symmetry emerges due to a violation of the thermal detailed balance by a zero-mean periodic driving and is optimized with frequency of driving, its amplitude, and temperature. Such optimized anomalous transport can be low dispersive and characterized by a large generalized Peclet number. Moreover, we show that overdamped subdiffusive ratchets can sustain a substantial load and do useful work. The corresponding thermodynamic efficiency decays algebraically in time since the useful work done against a load scales sublinearly with time following to the transport particle position, but the energy pumped by an external force scales with time linearly. Nevertheless, it can be transiently appreciably high and compare well with the thermodynamical efficiency of the normal diffusion overdamped ratchets on sufficiently long temporal and spatial scales.

Overdamped transport of particles in a periodic ratchet potential

We have employed overdamped Langevin dynamics to study the driven transport of particles in a tilted ratchet potential. The system subject to an applied direct force undergoes an asymmetrical dynamic transition from a static state to a sliding state at different bidirectional critical forces. When an additional alternating force is applied to the system, the mean velocity shows steps as the direct force increases. These plateaus appear whenever the system’s natural frequency given by the direct force matches an integer multiple of the alternating frequency, and are similar to the Shapiro steps on the current-voltage characteristics in rf-driven Josephson junctions. For a rocking ratchet without a direct force, the rectification effect occurs when the alternating force exceeds a certain critical value.

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.

Transport properties and current inversion by white Gaussian noise in a coupled ratchet model

We have found, by varying two parameters, several stationary trajectories in a system consisting in many elastically coupled particles that are placed in a periodic ratchet potential on a ring. The system is assumed to be over-damped and driven by an external potential that is periodic both in space and time. The transport properties of these orbits are quite different and their values are quantified. The symmetries allow us to study the orbits with and without the presence of thermal fluctuations and there is found current inversions due to the addition of white Gaussian noise.

Phase synchronization for two Brownian motors with bistable coupling on a ratchet

We study phase synchronization for a walker on a ratchet potential. The walker consist 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 deterministic and the stochastic dynamics of the center of mass of the walker in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues and show that the local maxima in the average velocity of the center of mass of the walker, both in the deterministic case and in the presence of noise, correspond to the borders of these Arnold tongues. In this way, we established a connection between optimal transport in ratchets and the phenomenon of phase synchronization.

Noise-induced transport in a rough ratchet potential

Several years ago Zwanzig considered the diffusion in a potential that is spatially rough due to hierarchical structure of protein. We extend this idea to the overdamped Brownian dynamics in a one-dimensional periodic and rough ratchet potential. A general expression is obtained for the effective current at the steady state. Variation in both current and efficiency has been studied with respect to the amplitude of the roughness and an external nonequilibrium, nonthermal driving force. It has been shown that roughness hinders current quite significantly. Our analysis is corroborated by detailed numerical simulations and may be useful in the context of laser switching of current through molecular wires.

Phase synchronization in tilted inertial ratchets as chaotic rotators

The phenomenon of phase synchronization for a particle in a periodic ratchet potential is studied. We consider the deterministic dynamics in the underdamped case where the inertia plays an important role since the dynamics can become chaotic. The ratchet potential is tilted due to a constant external force and is rocking by an external periodic forcing. This potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of the external periodic forcing; this oscillator then acquires an intrinsic frequency that can be locked with the frequency of the external driving. We introduced an instantaneous linear phase, using a set of discrete time markers, and the associated average frequency, and show that this frequency can be synchronized with the frequency of the driving. We calculate Arnold tongues in a two-dimensional parameter space and discuss their implications for the chaotic transport in ratchets. We show that the local maxima in the current correspond to the borders of these Arnold tongues; in this way we established a link between optimal transport in ratchets and phase synchronization.

Collective modes in a coupled ratchet model

We analyze a system consisting in many elastically coupled particles that are placed in a periodic ratchet potential on a ring. The system is assumed to be overdamped and driven by an external potential that is periodic both in space and time. The symmetries of the model allow to study the orbits with and without the presence of thermal fluctuations and for a changing intensity of the elastic coupling and the external driving force. We investigate the dependence of the transport current on the intensity of the elastic interaction. The direction of the current may be understood as resulting from the competition of collective transport modes in opposite directions and presents an inversion as the elastic coupling is increased.

WALKING ON RATCHETS WITH TWO BROWNIAN MOTORS

We analyze a model for a walker moving on an asymmetric periodic ratchet potential. This model is motivated by the properties of transport of the motor protein kinesin. The walker consists of two feet represented as two particles coupled nonlinearly through a double-well bistable potential. In contrast to linear coupling, the bistable potential admits a richer dynamics where the ordering of the particles can alternate during the walking. The transitions between the two stable points on the bistable potential, correspond to a walking with alternating particles. In our model, each particle is acted upon by independent white noises, modeling thermal noise, and additionally we have an external time-dependent force that drives the system out of equilibrium, allowing directed transport. In the equilibrium case, where only white noise is present, we perform a bifurcation analysis which reveals different walking patterns. In particular, we distinguish between two main walking styles: alternating and no alternating. These two ways of walking resemble the hand-over-hand and the inchworm walking in kinesin, respectively. Numerical simulations showed the existence of current reversals and significant changes in the effective diffusion constant. We obtained an optimal coherent transport, characterized by a maximum dimensionless ratio of the current and the effective diffusion (Péclet number), when the periodicity of the ratchet potential coincides with the equilibrium distance between the two particles.

SEGREGATION OF PARTICLES USING CHAOTIC RATCHETS

We address the problem of the chaotic transport of particles in an asymmetric periodic ratchet potential. We consider the case of deterministic rocking ratchets and analyze different regimes for the amplitude of rocking. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. We compare the dynamics of point particles and extended objects under the action of the ratchet potential and show that we can segregate particles according to its size.

Intermittency and deterministic diffusion in chaotic ratchets

We consider the problem of deterministic transport of particles in an asymmetric periodic ratchet potential of the rocking type. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. We calculate the bifurcation diagram as a function of the amplitude of forcing and analyze in detail the crisis bifurcation that leads to current reversals. Near this bifurcation we obtain intermittency and anomalous deterministic diffusion.

Current reversals in deterministic ratchets: points and dimers

We address the problem of the chaotic transport of point particles and rigid dimers in an asymmetric periodic ratchet potential. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. By a comparison between the bifurcation diagram and the current, we identify the origin of the multiple current reversals as bifurcations, usually from a chaotic to a periodic regime. We consider the dynamics of rigid dimers, as a function of size, extending in this way our previous results for point particles.

Ratchet motion induced by deterministic and correlated stochastic forces

We investigate analytically and through stochastic simulations the motion of a particle in a periodic nonsymmetric ratchet potential driven by time-correlated forces. We examine the extreme monochromatic deterministic case as well as the stochastic correlated noise case. Ratchet motion is found in both cases. In the correlated noise case we derive a single analytical expression for the induced current at large correlation times and compare it with numerical results. We also demonstrate numerically the occurrence of color-induced current reversal of a rigid dimer moving in a ratchet.