Brownian motion exhibiting absolute negative mobility

We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity is negative for F>0 and positive for F<0 (absolute negative mobility).     

Current reversal and mass separation of inertial Brownian motors in a two-noise ratchet

Transport of an inertial Brownian motor moving in an asymmetric periodic potential driven by an external force and correlated noises is investigated. Using the numerical algorithm, the asymptotic mean velocity (AMV) for characterizing directed transport is obtained. The effects of the external driving force f and the correlation λ between the two noises on the AMV are discussed. The results manifest: (1) the external driving force and the correlation between the two noises can lead to the phenomena like current reversal. (2) The competitions among the external driving force and the correlation between the two noises are necessary for current reversal, i.e., fλ>0. (3) Different directions of transport are found for different masses of the Brownian particles under the condition fλ>0. Therefore a theoretical study is suggested for separating Brownian particles according to their different masses in the ratchet system.     

Paradoxical Brownian motion in a microfluidic device: Absolute negative mobility

We report on a paradoxical migration mechanism in a microstructured lab-on-a-chip environment. The phenomenon is based on a subtle interplay between Brownian motion (thermal noise), a periodic and symmetric microstructure, and a biased AC electric field. The resulting non-linear dynamics far from thermal equilibrium gives rise to absolute negative mobility, i.e. a migrational transport, which is – both for negative and positive bias – always opposite to the net acting force, in good agreement between experiment and theory.     

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.     

Energetics of Brownian motors: a review

We review the literature on the energetics of Brownian motors, distinguishing between forced ratchets, chemical motors – driven out of equilibrium by differences of chemical potential, and thermal motors – driven by temperature differences. The discussion is focused on the definition of efficiency and the compatibility between the models and the laws of thermodynamics. Received: 13 November 2001 / Accepted: 10 January 2002 / Published online: 22 April 2002     

Brownian motors in the low-energy approximation: Classification and properties

We classify Brownian motors based on the expansion of their velocity in terms of the reciprocal friction coefficient. The two main classes of motors (with dichotomic fluctuations in homogeneous force and periodic potential energy) are characterized by different analytical dependences of their mean velocity on the spatial and temporal asymmetry coefficients and by different adiabatic limits. The competition between the spatial and temporal asymmetries gives rise to stopping points. The transition through these points can be achieved by varying the asymmetry coefficients, temperature, and other motor parameters, which can be used, for example, for nanoparticle segregation. The proposed classification separates out a new type of motors based on synchronous fluctuations in symmetric potential and applied homogeneous force. As an example of this type of motors, we consider a near-surface motor whose two-dimensional motion (parallel and perpendicular to the substrate plane) results from fluctuations in external force inclined to the surface.     

Quantum features of Brownian motors and stochastic resonance

We investigate quantum Brownian motion sustained transport in both, adiabatically rocked ratchet systems and quantum stochastic resonance (QSR). Above a characteristic crossover temperature T(0) tunneling events are rare; yet they can considerably enhance the quantum-noise-driven particle current and the amplification of signal output in comparison to their classical counterparts. Below T(0) tunneling prevails, thus yielding characteristic novel quantum transport phenomena. For example, upon approaching T=0 the quantum current in Brownian motors exhibits a tunneling-induced reversal, and tends to a finite limit, while the classical result approaches zero without such a change of sign. As a consequence, similar current inversions generated by quantum effects follow upon variation of the particle mass or of its friction coefficient. Likewise, in this latter regime of very low temperatures the tunneling dynamics becomes increasingly coherent, thus suppressing the semiclassically predicted QSR. Moreover, nonadiabatic driving may cause driving-induced coherences and quantized resonant transitions with no classical analog. (c) 1998 American Institute of Physics.     

Inter-valley repopulation and negative differential mobility in Si at 8°K

The negative differential mobility in Si at 8°K has been theoretically interpreted in terms of inter-valley repopulation among equivalent minima. The mean energies of electrons has been found to be extremely sensitive to inter-valley mechanism producing a weaker repopulation from hot to cold valleys. Lattice ohmic mobility seems to be affected by non Coulomb impurities.     

Brownian motors: Joint effect of non-Gaussian noise and time asymmetric forcing

Previous works have shown that time asymmetric forcing on the one hand, as well as non-Gaussian noises on the other, can separately enhance the efficiency and current of a Brownian motor. Here, we study the result of subjecting a Brownian motor to both effects simultaneously. Our results have been compared with those obtained for the Gaussian white noise regime in the adiabatic limit. We find that, although the inclusion of the time asymmetry parameter increases the efficiency value up to a certain extent, for the present case this increase is much less appreciable than in the white noise case. We also present a comparative study of the transport coherence in the context of colored noise. Though the efficiency in some cases becomes higher for the non-Gaussian case, the Péclet number is always higher in the Gaussian colored noise case than in the white noise as well as non-Gaussian colored noise cases.     

Double-temperature ratchet model and current reversal of coupled Brownian motors

On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal the dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional transport of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asymmetric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.     

Anomalous mobility and current reversals in inertial deterministic ratchets

We analyze the transport properties of inertial deterministic rocking ratchets in the presence of an external constant force. For small values of this load, we can obtain a positive current for a negative load, and vice versa. This phenomenon, in which the direction of the current is opposed to the sign of the external force, is a signature of anomalous negative mobility. We show that this anomalous mobility is possible in the deterministic case, and explain this phenomenon as current reversals associated to bifurcations in an inertial deterministic rocking ratchet in the presence of an external load.     

Efficiency of Interacting Brownian Motors: Improved Mean-Field Treatment

The “reversible ratchet” model of interacting Brownian motors, introduced by us earlier, is investigated using a one-site approximation of a mean-field type. We confirm the effect of enhanced efficiency due to repulsive interaction and we provide arguments suggesting that the enhancement is of energetic, rather than entropic, origin. We also check the validity of the fluctuation theorem for stationary particle current.     

Current and efficiency enhancement in Brownian motors driven by non Gaussian noises

We study Brownian motors driven by colored non Gaussian noises, both in the overdamped regime and in the case with inertia, and analyze how the departure of the noise distribution from Gaussian behavior can affect its behavior. We analyze the problem from two alternative points of view: one oriented mainly to possible technological applications and the other more inspired in natural systems. In both cases we find an enhancement of current and efficiency due to the non-Gaussian character of the noise. We also discuss the possibility of observing an enhancement of the mass separation capability of the system when non-Gaussian noises are considered.Received: 8 July 2004, Published online: 30 September 2004PACS: 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 05.40.Jc Brownian motion - 87.16.Uv Active transport processes; ion channels     

Ratchet motion and current reversal of coupled Brownian motors in pulsating symmetric potentials

In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two particles can induce symmetry breaking and consequently collective directed motion. Moreover, the direction of motion can be reversed under certain conditions. The dependence of directed current on various parameters is systematically studied. reverse motion can be achieved by modulating the coupling free length and the phase shift of the pulsating potential. The dynamical mechanism of these transport properties is understood in terms of the effective-potential theory and the space-time transformation invariance. The directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.     

Mesoscopic resistive switch: non-volatility,hysteresis and negative differential resistance

We show how a simple model nanoswitch can perform as a memory resistor. Its resistance is determined by electron tunneling through a nanoparticle diffusing around one or more potential minima located between the electrodes in the presence of Joule’s heat dissipation. In the case of a single potential minimum, we observe hysteresis of the resistance at finite applied currents and negative differential resistance. For two (or more) minima the switching mechanism is non-volatile, meaning that the memristor can switch to a resistive state of choice and stay there. Moreover, the noise spectra of the switch exhibit 1/f ² → 1/f crossover, in agreement with recent experimental results.     

Positive and negative differential resistance in electrical conductors

A phase transition from one conducting state to another and the appearance of positive and negative differential resistance in the current-voltage characteristic is investigated experimentally for the gap instability in nonequilibrium superconductors and the avalanche breakdown in extrinsic semiconductors. Additional observation of spatial current structures in the transition regime of both solid-state systems stimulates a simple model approach connecting these spatial patterns to the measured current-voltage characteristics. Based on the underlying experimental situations considered, our model is extended to the framework of four substantial cases.     

Correlation functions and differential mobility in the hot electron problem

A projection operator technique is developed to study the far from équilibrium steady state transport problem. It is shown that the results previously obtained by Monte Carlo methods for the various correlation functions and differential mobility are satisfactorily predicted analytically. The temporal behavior of the velocity autocorrelation function predicted previously by intuitive arguments is formally justified.