Diffusion enhancement in a periodic potential under high-frequency space-dependent forcing

Temperature anomalies of oscillating diffusion in ac-driven periodic systems

We analyze the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low-friction regime in which the diffusion coefficient shows giant damped quasiperiodic oscillations as a function of the amplitude of the time-periodic force [I. G. Marchenko et al., Chaos 32, 113106 (2022)1054-150010.1063/5.0117902]. We find out that when temperature grows the diffusion coefficient increases at its minima; however, it decreases at the maxima within a finite temperature window. This curious behavior is explained in terms of the deterministic dynamics perturbed by thermal fluctuations and mean residence time of the particle in the locked and running trajectories. We demonstrate that temperature dependence of the diffusion coefficient can be accurately reconstructed from the stationary probability to occupy the running trajectories.

Roughness in the periodic potential enhances transport in a driven inertial ratchet

We study the effects of roughness in the asymmetric periodic potential on the transport and diffusion of an inertial Brownian particle driven by a time-periodic force in a Gaussian environment. We find that moderate roughness leads to the loss of transient anomalous diffusion, and it helps to establish normal diffusion in the weak noise limit. We uncover a contrasting effect of roughness on the transport of particles in the weak and moderate to large noise limit. In the weak noise limit, small amplitude roughness results in the increase of directed transport, whereas in the moderate to large noise limit, roughness hinders transport. The deterministic dynamics of the system reveals that the purely periodic system under smooth potential transits into a chaotic system due to the moderate roughness in the potential. Therefore our calculations demonstrate the constructive role of roughness in the transport of particles in the inertial regime.

Enhanced diffusion on oscillating surfaces through synchronization

The diffusion of molecules and clusters under nanoscale confinement or absorbed on surfaces is the key controlling factor in dynamical processes such as transport, chemical reaction, or filtration. Enhancing diffusion could benefit these processes by increasing their transport efficiency. Using a nonlinear Langevin equation with an extensive number of simulations, we find a large enhancement in diffusion through surface oscillation. For helium confined in a narrow carbon nanotube, the diffusion enhancement is estimated to be over three orders of magnitude. A synchronization mechanism between the kinetics of the particles and the oscillating surface is revealed. Interestingly, a highly nonlinear negative correlation between diffusion coefficient and temperature is predicted based on this mechanism, and further validated by simulations. Our results provide a general and efficient method for enhancing diffusion, especially at low temperatures.

Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex

To date investigations of the dynamics of driven colloidal systems have focused on hydrodynamic interactions and often employ optical (laser) tweezers for manipulation. However, the optical fields that provide confinement and drive also result in electrodynamic interactions that are generally neglected. We address this issue with a detailed study of interparticle dynamics in an optical ring vortex trap using 150-nm diameter Ag nanoparticles. We term the resultant electrodynamically interacting nanoparticles a driven optical matter system. We also show that a superior trap is created by using a Au nanoplate mirror in a retroreflection geometry, which increases the electric field intensity, the optical drive force, and spatial confinement. Using nanoparticles versus micron sized colloids significantly reduces the surface hydrodynamic friction allowing us to access small values of optical topological charge and drive force. We quantify a further 50% reduction of hydrodynamic friction when the nanoparticles are driven over the Au nanoplate mirrors versus over a mildly electrostatically repulsive glass surface. Further, we demonstrate through experiments and electrodynamics-Langevin dynamics simulations that the optical drive force and the interparticle interactions are not constant around the ring for linearly polarized light, resulting in a strong position-dependent variation in the nanoparticle velocity. The nonuniformity in the optical drive force is also manifest as an increase in fluctuations of interparticle separation, or effective temperature, as the optical driving force is increased. Finally, we resolve an open issue in the literature on periodic modulation of interparticle separation with comparative measurements of driven 300-nm-diameter polystyrene beads that also clearly reveal the significance of electrodynamic forces and interactions in optically driven colloidal systems. Therefore, the modulations in the optical forces and electrodynamic interactions that we demonstrate should not be neglected for dielectric particles and might give rise to some structural and dynamic features that have previously been attributed exclusively to hydrodynamic interactions.

Multiple current reversals and diffusion enhancement in a symmetrical periodic potential

Transport and diffusion of Brownian particles in a symmetrical periodic potential were investigated for both overdamped and underdamped cases, where the ratchet potential is driven by an external unbiased time periodic force and correlation between thermal and potential fluctuations. It is shown that the correlation between two noises breaks the symmetry of the potential to generate motion of the Brownian particles in particular direction, and the current can reverse its direction by changing the sign of the noise correlation. For the overdamped case, the systemic parameters only induce the directed current, and the noise correlation suppresses the diffusion of the overdamped Brownian particles. However for the underdamped case, the current reverses its direction multiple times with increasing the systemic parameters, i.e., the multiple current reversal is observed, and the noise negative correlation suppresses the diffusion of the underdamped Brownian particles, while the noise positive correlation enhances it.

Artificial sieves for quasimassless particles

Brownian motion on a symmetric vibrated periodic substrate is shown to be extremely sensitive to the particle mass even in the regime of large damping. This phenomenon is the most apparent for high vibration frequencies, a condition of technological interest, which is investigated here both analytically and numerically. When plotted versus the damping constant, both the particle mobility and the diffusion coefficient develop sharp (correlated) peaks, thus suggesting efficient schemes for separating submicron particles according to their mass or geometry.

Bifurcations and sudden current change in ensembles of classically chaotic ratchets

Mateos [Phys. Rev. Lett. 84, 258 (2000)] conjectured that current reversal in a classical deterministic ratchet is associated with bifurcations from chaotic to periodic regimes. This is based on the comparison of the current and the bifurcation diagram as a function of a given parameter for a periodic asymmetric potential. Barbi and Salerno [Phys. Rev. E 62, 1988 (2000)] have further investigated this claim and argue that, contrary to Mateos' claim, current reversals can occur also in the absence of bifurcations. Barbi and Salerno's studies are based on the dynamics of one particle rather than the statistical mechanics of an ensemble of particles moving in the chaotic system. The behavior of ensembles can be quite different, depending upon their characteristics, which leaves their results open to question. In this paper we present results from studies showing how the current depends on the details of the ensemble used to generate it, as well as conditions for convergent behavior (that is, independent of the details of the ensemble). We are then able to present the converged current as a function of parameters, in the same system as Mateos as well as Barbi and Salerno. We show evidence for current reversal without bifurcation, as well as bifurcation without current reversal. We conjecture that it is appropriate to correlate abrupt changes in the current with bifurcation, rather than current reversals, and show numerical evidence for our claims.