Stimulated diffusion of an adsorbed dimer

Diffusion enhancement and autoparametric resonance

The possibility of an autoparametric resonance in an isolated many-particle system induces a specific behavior of the particles in the presence of thermal noise. In particular, the variance associated with a resonant mode, and consequently that of the associated particles, is strongly increased compared to what it would have in the absence of parametric resonance. In this paper we consider a dimer submitted to a periodic potential for which there are only two modes, the center of mass motion and the internal vibration mode. This is the simplest system which is dynamically rich enough to exhibit an autoparametric excitation of the internal vibrations by the center of mass motion. The consequences of this autoparametric excitation on the particles diffusion will be discussed according to the stiffness of the interaction and to the initial energy of the dimer, the relevant parameters which characterize this dynamics.

Stochastic models for surface diffusion of molecules

We derive a stochastic model for the surface diffusion of molecules, starting from the classical equations of motion for an N-atom molecule on a surface. The equation of motion becomes a generalized Langevin equation for the center of mass of the molecule, with a non-Markovian friction kernel. In the Markov approximation, a standard Langevin equation is recovered, and the effect of the molecular vibrations on the diffusion is seen to lead to an increase in the friction for center of mass motion. This effective friction has a simple form that depends on the curvature of the lowest energy diffusion path in the 3N-dimensional coordinate space. We also find that so long as the intramolecular forces are sufficiently strong, memory effects are usually not significant and the Markov approximation can be employed, resulting in a simple one-dimensional model that can account for the effect of the dynamics of the molecular vibrations on the diffusive motion.

Molecular shape and the energetics of chemisorption: from simple to complex energy landscapes

We enumerate all local minima of the energy landscape for model rigid adsorbates characterized by three or four equivalent binding sites (e.g., thiol groups) on a close-packed (111) surface of a face-centered-cubic crystal. We show that the number of energy minima increases linearly with molecular size with a rate of increase that depends on the degree of registry between the molecule shape and the surface structure. The sparseness of energy minima and the large variations in the center-of-mass positions of these minima vs molecular size for molecules that are incommensurate with the surface suggests a strong coupling in these molecules between surface mobility and shape or size fluctuations resulting from molecular vibrations. We also find that the variation in the binding energy with respect to molecular size decreases more rapidly with molecular size for molecules with a higher degree of registry with the surface. This indicates that surface adsorption should be better able to distinguish molecules by size if the molecules are incommensurate with the surface.

Dimer motion on a periodic substrate: spontaneous symmetry breaking and absolute negative mobility

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.

Exploring the dynamics of dimer crossing over a Kramers type potential

We explore the escape rate of a dimer crossing a potential barrier using both analytical and numerical approaches. We find that for small coupling strength k, the barrier hopping can be well approximated by a two step reaction scheme where one monomer hops over the barrier and is then followed by the other. In this regime the escape rate increases with k showing that the cooperativity between monomers enhances the crossing rate. However, in the limit of large coupling strength, applying the method of adiabatic elimination, we find that the escape rate is a decreasing function of k. Thus, we find that the escape rate is a non-monotonic function of the spring constant which is peaked at an optimal coupling strength. Furthermore, in the presence of a weak periodic signal, we show that the system response to the periodic signal is pronounced at a particular spring constant showing the dimer can be transported rapidly across the reaction coordinate in a half period.

From collective periodic running states to completely chaotic synchronised states in coupled particle dynamics

We consider the damped and driven dynamics of two interacting particles evolving in a symmetric and spatially periodic potential. The latter is exerted to a time-periodic modulation of its inclination. Our interest is twofold: First, we deal with the issue of chaotic motion in the higher-dimensional phase space. To this end, a homoclinic Melnikov analysis is utilised assuring the presence of transverse homoclinic orbits and homoclinic bifurcations for weak coupling allowing also for the emergence of hyperchaos. In contrast, we also prove that the time evolution of the two coupled particles attains a completely synchronised (chaotic) state for strong enough coupling between them. The resulting "freezing of dimensionality" rules out the occurrence of hyperchaos. Second, we address coherent collective particle transport provided by regular periodic motion. A subharmonic Melnikov analysis is utilised to investigate persistence of periodic orbits. For directed particle transport mediated by rotating periodic motion, we present exact results regarding the collective character of the running solutions entailing the emergence of a current. We show that coordinated energy exchange between the particles takes place in such a manner that they are enabled to overcome--one particle followed by the other--consecutive barriers of the periodic potential resulting in collective directed motion.

Current control in a tilted washboard potential via time-delayed feedback

We consider the motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e., a current. It is demonstrated that with an additional time-delayed feedback term, the particle current can be reversed against the direction of the bias. The control function induces a ratchetlike effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to the current control in a wide temperature range.

Ratchet effect of a dimer with broken friction symmetry in a symmetric potential

The one-dimensional overdamped Brownian motion of a dimer consisting of two harmonically interacting components is considered. Both components are coupled to the same heat bath and feel the same spatially periodic symmetric potential, whose amplitude is modulated periodically in time. The friction coefficients may differ between dimer components, thus breaking the dynamical symmetry of the system. In the absence of any external bias, a ratchet effect (directed transport) arises generically. Two accurate approximations for the dimer's velocity and diffusion coefficient are obtained for weak and strong couplings. The velocity of the system can be maximized for each direction by adding an optimal amount of noise and by tuning the driving frequency to an optimal value. Furthermore, there exist two optimal coupling strengths at which the velocity is the largest.

Interaction-controlled Brownian motion in a tilted periodic potential

The drift and diffusion of a few interacting, overdamped Brownian particles in a tilted periodic potential are studied analytically and numerically. Both quantities exhibit a complex multipeaked structure as a function of the equilibrium interparticle separation. Upon variation of the interaction strength, both drift and diffusion may exhibit a nonmonotonic, resonancelike behavior.

Resonancelike phenomena in the mobility of a chain of nonlinear coupled oscillators in a two-dimensional periodic potential

We study the Langevin dynamics of a two-dimensional discrete oscillator chain absorbed on a periodic substrate and subjected to an external localized point force. Going beyond the commonly used harmonic bead-spring model, we consider a nonlinear Morse interaction between the next-nearest neighbors. We focus interest on the activation of directed motion instigated by thermal fluctuations and the localized point force. In this context the local transition states are identified and the corresponding activation energies are calculated. It is found that the transport of the chain in point force direction is determined by stepwise escapes of a single unit or segments of the chain due to the existence of multiple locally stable attractors. The nonvanishing net current of the chain is quantitatively assessed by the value of the mobility of the center of mass. It turns out that the latter as a function of the ratio of the competing length scales of the system, that is the period of the substrate potential and the equilibrium distance between two chain units, shows a resonance behavior. More precisely there exists a set of optimal parameter values maximizing the mobility. Interestingly, the phenomenon of negative resistance is found, i.e., the mobility possesses a minimum at a finite value of the strength of the thermal fluctuations for a given overcritical external driving force.

Transition between locked and running states for dimer motion induced by periodic external driving

We study the motion of a dimer in a one-dimensional spatially periodic washboard potential. The tilt of the latter is time-periodically modulated by an ac field. We focus interest on the detrapping of the (static) ground state solution of the dimer caused by the ac field. Moreover, we demonstrate that slow tilt modulations not only induce a trapping-detrapping transition but drive the dimer dynamics into a regime of transient long-range running states. Most strikingly, the motion proceeds then unidirectionally, so that the dimer covers huge distances regardless of the fact that the bias force in the driven system vanishes on the average. We elucidate the underlying dynamics in phase space and associate long-lasting running states with the motion in ballistic channels occurring due to stickiness to invariant tori.

Dynamics of a dimer in a symmetric potential: ratchet effect generated by an internal degree of freedom

The one-dimensional dynamics of a dimer consisting of two harmonically coupled components is considered. The mutual distance between the dimer components plays the role of an internal degree of freedom. Both components are in contact with the same heat bath and are coupled to a spatially periodic, symmetric potential, whose amplitude is modulated periodically in time and whose coupling strength is different for the two components. In the absence of any external bias, a ratchet effect (directed transport) arises generically unless the mutual coupling of the dimer components tends to zero or infinity. In other words, the ratchet effect is generated by the internal degree of freedom. An accurate analytical approximation for the dimer's velocity and diffusion coefficient is obtained. The velocity of the system is maximized by adding an optimal amount of noise and by tuning the driving frequency to an optimal value. Furthermore, there exists an optimal coupling strength at which the velocity is the largest.

Dimer diffusion in a washboard potential

The transport of a dimer, consisting of two Brownian particles bounded by a harmonic potential, moving on a periodic substrate is investigated both numerically and analytically. The mobility and diffusion of the dimer center of mass present distinct properties when compared with those of a monomer under the same transport conditions. Both the average current and the diffusion coefficient are found to be complicated nonmonotonic functions of the driving force. The influence of dimer equilibrium length, coupling strength, and damping constant on the dimer transport properties are also examined in detail.

Resonant diffusion on modulated surfaces

Some theoretical methods for description of the diffusion on modulated surfaces are reviewed. A general formula for calculation of the diffusion coefficient of a particle moving in the field of a periodic potential is developed, which takes into account both the potential barrier effect and the dependence of the friction coefficient on the potential. The application of the theory to the diffusion of dimers on solid surfaces reveals a non-monotonous dependence of the diffusion coefficient on the ratio between the dimer and solid spatial parameters. This resonant dependence sometimes can be suppressed by the rotations and vibrations on the dimer. In the present theory the latter are described via an adiabatic approach.