Giant diffusion and coherent transport in tilted periodic inhomogeneous systems

Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond

The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that can be modeled in the framework of Langevin dynamics. Our main focus centers on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds, we consider a number of physical situations outside of free Brownian motion and end by surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.

Brownian ratchets: How stronger thermal noise can reduce diffusion

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model.

Diffusion and mobility of anisotropic particles in tilted periodic structures

We numerically investigated the transport of anisotropic particles in tilted periodic structures. The diffusion and mobility of the particles demonstrate distinct behaviors dependence on the shape of the particles. In two-dimensional (2D) periodic potentials, we find that the mobility is influenced a little by the anisotropy of the particle, while the diffusion increases monotonically with the increasing of the particle anisotropy for large enough biased force. However, due to the sensitivity of the channels for the particle anisotropy, the transport in smooth channels is obviously different from that in energy potentials. The mobility decreases monotonically with the increasing of the particle anisotropy, while the diffusion can be a non-monotonic function of the particle anisotropy with a peak under appropriate biased force.

Effective diffusion coefficient in tilted disordered potentials: optimal relative diffusivity at a finite temperature

In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case of random potentials resulting from the interaction of a particle with a "random polymer". In our model the polymer is made up, by means of some stochastic process, of monomers that can be taken from a finite or countable infinite set of possible monomer types. For the case of uncorrelated random polymers we found that the diffusion coefficient exhibits a non-monotonous behavior as a function of the noise intensity. Particularly interesting is the fact that the relative diffusivity becomes optimal at a finite temperature, a behavior which is reminiscent of stochastic resonance. We explain this effect as an interplay between the deterministic and noisy dynamics of the system. We also show that this behavior of the diffusion coefficient at a finite temperature is more pronounced for the case of weakly disordered potentials. We test our findings by means of numerical simulations of the corresponding Langevin dynamics of an ensemble of noninteracting overdamped particles diffusing on uncorrelated random potentials.

Diffusion in a tilted periodic potential with entropic barriers

Diffusion of Brownian particles in a periodic channel is investigated in the presence of a tilted spatially periodic potential. Reduction of spatial dimensionality from two or three dimensions to an effective one-dimensional system entails the appearance of not only an entropic barrier but also an effective diffusion coefficient. It is found that diffusion exhibits striking features which are different from those observed in the previous cases. The interplay between the potential barriers and entropic barriers makes the phenomena richer. Remarkably, two temperature values exist at which the Peclet number takes its maximum.

Quantum transport in a periodic symmetric potential of a driven quantum system

A system-reservoir nonlinear coupling model has been proposed to the situation when the system is driven externally by a random force and the associated bath is kept in thermal equilibrium, in an attempt to put forth a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum Langevin equation in the overdamped limit (quantum Smoluchowski equation). We then obtain the analytical expression for phase induced quantum current in a periodic potential when the external noise has finite correlation time and explore the dependence of the current on various parameters related to the external noise, for example, the noise strength.

Phase induced current in presence of nonequilibrium bath: A quantum approach

Based on a system-reservoir nonlinear coupling model, where the associated bath is externally driven by a fluctuating force, we present a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum (Markovian) Langevin equation in overdamped limit when the associated bath is in nonequilibrium state. We then explore the possibility of observing a quantum current when the bath is modulated by white noise, the phenomena which is absent in the classical regime.

Enhancing mixing and diffusion with plastic flow

We use numerical simulations to examine two-dimensional particle mixtures that strongly phase separate in equilibrium. When the system is externally driven in the presence of quenched disorder, plastic flow occurs in the form of meandering and strongly mixing channels. In some cases, this can produce a fast and complete mixing of previously segregated particle species, as well as an enhancement of transverse diffusion even in the absence of thermal fluctuations. We map the mixing phase diagram as a function of external driving and quenched disorder parameters.

Directed motion in a periodic potential of a quantum system coupled to a heat bath driven by a colored noise

A system-reservoir nonlinear coupling model is proposed for a quantum system when the associated bath is not in thermal equilibrium but is modulated by an external colored noise, to present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Langevin description. Consequently, the Fokker-Planck equation in position space, valid in the overdamped limit, for multiplicative colored noise is constructed to explore the possibility of observing a quantum current and dependence of the current on various parameters of external noise is examined.

State transition of a non-Ohmic damping system in a corrugated plane

Anomalous transport of a particle subjected to non-Ohmic damping of the power delta in a tilted periodic potential is investigated via Monte Carlo simulation of the generalized Langevin equation. It is found that the system exhibits two relative motion modes: the locked state and the running state. In an environment of sub-Ohmic damping (0<delta<1) , the particle should transfer into a running state from a locked state only when local minima of the potential vanish; hence a synchronization oscillation occurs in the particle's mean displacement and mean square displacement (MSD). In particular, the two motion modes are allowed to coexist in the case of super-Ohmic damping (1<delta<2) for moderate driving forces, namely, where double centers exist in the velocity distribution. This causes the particle to have faster diffusion, i.e., its MSD reads <Deltax(2)(t)>=2D_(eff)(delta){t(delta_eff} . Our result shows that the effective power index delta_(eff) can be enhanced and is a nonmonotonic function of the temperature and the driving force. The mixture of the two motion modes also leads to a breakdown of the hysteresis loop of the mobility.

Quantum diffusion in biased washboard potentials: strong friction limit

Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the diffusive behavior by evaluating the effective diffusion coefficient together with the corresponding Peclet number. Corrections due to quantum effects, such as quantum tunneling and quantum fluctuations, are shown to substantially enhance the effectiveness of diffusive transport if only the thermostat temperature resides within an appropriate interval of intermediate values.

Performance characteristics of Brownian motors

Brownian motors are nonequilibrium systems that rectify thermal fluctuations to achieve directed motion, using spatial or temporal asymmetry. We provide a tutorial introduction to this basic concept using the well-known example of a flashing ratchet, discussing the micro- to nanoscopic scale on which such motors can operate. Because of the crucial role of thermal noise, the characterization of the performance of Brownian motors must include their fluctuations, and we review suitable performance measures for motor coherency and efficiency. Specifically, we highlight that it is possible to determine the energy efficiency of Brownian motors by measuring their velocity fluctuations, without detailed knowledge of the motor function and its energy input. Finally, we exemplify these concepts using a model for an artificial single-molecule motor with internal degrees of freedom.

Diffusion and coherence in tilted piecewise linear double-periodic potentials

In the present paper we study the overdamped motion of Brownian particles in tilted periodic piecewise linear potentials of two maxima per period. This system allows one to observe additional phenomena with respect to the case of single-periodic potentials. We show that for certain types of potentials the effective diffusion coefficient D (F) can be enhanced or suppressed compared to the simple sawtooth case. As the most unexpected result it is found that the curve of diffusion coefficient vs tilt can have two maxima. In the region of Poissonian hopping processes we demonstrate the possibility to have a resonantlike peak in the Péclet number Pe(F) . At the tilting force corresponding to the maximum of Pe(F) , the curve of Péclet number vs temperature possesses two maxima.

Brownian rectifiers in the presence of temporally asymmetric unbiased forces

The efficiency of energy transduction in a temporally asymmetric rocked ratchet is studied. Time asymmetry favors current in one direction and suppresses it in the opposite direction due to which large efficiency approximately 50% is readily obtained. The spatial asymmetry in the potential together with system inhomogeneity may help in further enhancing the efficiency. Fine tuning of system parameters considered leads to multiple current reversals even in the adiabatic regime.

Diffusion and current of Brownian particles in tilted piecewise linear potentials: amplification and coherence

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the nonmonotonic behavior of the diffusion coefficient as a function of temperature are determined. The diffusion coefficient and coherence level are found to be extremely sensitive to the asymmetry of the potential. It is established that at the values of the external force, for which the enhancement of diffusion is most rapid, the level of coherence has a wide plateau at low temperatures with the value of the Péclet factor 2. An interpretation of the amplification of diffusion in comparison with free thermal diffusion in terms of probability distribution is proposed.

Brownian particle in an optical potential of the washboard type

Experimental observations of the fluctuation-driven net transport of silica microspheres are presented in a two-dimensional optical potential of circular symmetry created by a Bessel light beam. The optical field is tailored to break symmetry and create a static tilted periodic (washboard) potential. As the tilt of potential exceeds a threshold, a transition between locked and running modes is observed. The running mode manifests itself by the rapid accumulation of particles at the beam center.