Single-file diffusion on a periodic substrate

Controlling colloidal flow through a microfluidic Y-junction

Microscopic particles flowing through narrow channels may accumulate near bifurcation points provoking flow reduction, clogging and ultimately chip breakage in a microfluidic device. Here we show that the full flow behavior of colloidal particles through a microfluidic Y-junction can be controlled by tuning the pair interactions and the degree of confinement. By combining experiments with numerical simulations, we investigate the dynamic states emerging when magnetizable colloids flow through a symmetric Y-junction such that a single particle can pass through both gates with the same probability. We show that clogging, induced by the inevitable presence of a stagnation point, can be avoided by repulsive interactions. Moreover we tune the pair interactions to steer branching into the two channels: attractive particles are flowing through the same gate, while repulsive colloids alternate between the two gates. Even details of the particle assembly such as buckling at the exit gate are tunable by the interactions and the channel geometry.

Single-file diffusion in spatially inhomogeneous systems

We study the effect of spatially varying potential and diffusivity on the dispersion of a tracer particle in single-file diffusion. Noninteracting particles in such a system exhibit normal diffusion at late times, which is characterized by an effective diffusion constant D_{eff}. Here we demonstrate the physically appealing result that the dispersion of single-file tracers in this system has the same long-time behavior as that for Brownian particles in a spatially homogeneous system with constant diffusivity D_{eff}. Our results are based on a late-time analysis of the Fokker-Planck equation, motivated by the mathematical theory of homogenization. The findings are confirmed by numerical simulations for both annealed and quenched initial conditions.

Universal Relation between Entropy and Kinetics

Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle configurations. It is universal and applicable to steady states arbitrarily far from thermodynamic equilibrium. Applying the general relation to diffusive dynamics yields a relation between the entropy and the (normal or anomalous) diffusion coefficient. The relation can be used to obtain useful bounds for the late-time diffusion coefficient from the calculated steady-state entropy or, conversely, to estimate the entropy based on measured diffusion coefficients. We demonstrate the validity and usefulness of the relation through several examples and discuss its broad range of applications, in particular, for systems far from equilibrium.

Brownian particles in periodic potentials: Coarse-graining versus fine structure

We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than the periodicity of the potential, the packet of spreading particles, all starting from a common origin, converges to a normal distribution centered at the origin with a mean-squared displacement that grows as 2D^{*}t, with an effective diffusion constant that is smaller than that of a freely diffusing particle. We examine the interplay between this coarse-grained description and the fine structure of the density, which is given by the Boltzmann-Gibbs (BG) factor e^{-V(x)/k_{B}T}, the latter being nonnormalizable. We explain this result and construct a theory of observables using the Fokker-Planck equation. These observables are classified as those that are related to the BG fine structure, like the energy or occupation times, while others, like the positional moments, for long times, converge to those of the large-scale description. Entropy falls into a special category as it has a coarse-grained and a fine structure description. The basic thermodynamic formula F=TS-E is extended to this far-from-equilibrium system. The ergodic properties are also studied using tools from infinite ergodic theory.

Nonequilibrium master equation for interacting Brownian particles in a deep-well periodic potential

Employing a creation and annihilation operator formulation, we derive an approximate many-body master equation describing discrete hopping from the more general continuous description of Brownian motion on a deep-well nonequilibrium periodic potential. The many-body master equation describes interactions of arbitrary strength and range arising from a "top-hat" two-body interaction potential. We show that this master equation reduces to the well-known asymmetric simple exclusion process and the zero range process in certain regimes. We also use the creation and annihilation operator formalism to derive results for the steady-state drift and the number fluctuations in special cases, including the unexplored limit of weak interparticle interactions.

Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion

In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the nonequilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the timescale on which a finite system can exhibit anomalous kinetics. In particular, we demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied. Conversely, the TUR bounds the onset of superdiffusion in the active comb model. Remarkably, the fluctuations in a comb model evolving from a steady state behave anomalously as soon as detailed balance is broken. Our work establishes a link between stochastic thermodynamics and the field of anomalous dynamics that will fertilize further investigations of thermodynamic consistency of anomalous diffusion models.

Transport of coupled particles in rough ratchet driven by Lévy noise

This paper studies the transport of coupled particles in a tilted rough ratchet potential. The relationship between particles transport and roughness, noise intensity, external force, coupling strength, and free length is explored numerically by calculating the average velocity of coupled particles. Related investigations have found that rough potential can accelerate the process of crossing the barrier by increasing the particles velocity compared with smooth potential. It is based on the fact that the roughness on the potential surface is like a "ladder," which helps particles climb up and blocks them from sliding down. Moreover, superimposing an appropriate external force on the coupled particles or strengthening the Lévy noise leads to the particles velocity to increase. It is worth emphasizing that when the external force is selected properly, an optimal roughness can be found to maximize the particles velocity. For a given roughness, an optimal coupling coefficient is discovered to match the maximum velocity. And once the coupling coefficient is greater than the optimal value, the particles velocity drops sharply to zero. Furthermore, our results also indicate that choosing an appropriate free length between particles can also speed up transport.

Transition of multidiffusive states in a biased periodic potential

We study a frequency-dependent damping model of hyperdiffusion within the generalized Langevin equation. The model allows for the colored noise defined by its spectral density, assumed to be proportional to ω^{δ-1} at low frequencies with 0<δ<1 (sub-Ohmic damping) or 1<δ<2 (super-Ohmic damping), where the frequency-dependent damping is deduced from the noise by means of the fluctuation-dissipation theorem. It is shown that for super-Ohmic damping and certain parameters, the diffusive process of the particle in a titled periodic potential undergos sequentially four time regimes: thermalization, hyperdiffusion, collapse, and asymptotical restoration. For analyzing transition phenomenon of multidiffusive states, we demonstrate that the first exist time of the particle escaping from the locked state into the running state abides by an exponential distribution. The concept of an equivalent velocity trap is introduced in the present model; moreover, reformation of ballistic diffusive system is also considered as a marginal situation but does not exhibit the collapsed state of diffusion.

Single file dynamics in soft materials

The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-sections comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a single file, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membranes, just to mention a few examples. Albeit introduced in 1965s, over the last decade the classical notion of SF dynamics has been generalised to account for a more realistic modelling of the particle properties, file geometry, particle-particle and channel-particle interactions, which paves the way to remarkable applications of the SF model, for instance, in the technology of bio-integrated nanodevices. We provide here a comprehensive review of the recent advances in the theory of SF dynamics with the purpose of spurring further experimental work.

Single-file and normal diffusion of magnetic colloids in modulated channels

Diffusive properties of interacting magnetic dipoles confined in a parabolic narrow channel and in the presence of a periodic modulated (corrugated) potential along the unconfined direction are studied using Brownian dynamics simulations. We compare our simulation results with the analytical result for the effective diffusion coefficient of a single particle by Festa and d'Agliano [Physica A 90, 229 (1978)] and show the importance of interparticle interaction on the diffusion process. We present results for the diffusion of magnetic dipoles as a function of linear density, strength of the periodic modulation and commensurability factor.

Analytical calculation of four-point correlations for a simple model of cages involving numerous particles

Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter σ) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and the overlap-density-based generalized susceptibility are calculated analytically by way of the Lagrangian correlation of the interparticulate space, instead of the Eulerian correlation of density that is commonly used in the standard mode-coupling theory. In regard to the mean square displacement, the linear analysis reproduces the established result on the asymptotic subdiffusive behavior of the system. A finite-time correction is given by incorporating the effect of entropic nonlinearity with a Lagrangian version of mode-coupling theory. The notorious difficulty in derivation of the mode-coupling theory concerning violation of the fluctuation-dissipation theorem is found to disappear by virtue of the Lagrangian description. The Lagrangian description also facilitates analytical calculation of four-point correlations in the space-time, such as the two-particle displacement correlation. The two-particle displacement correlation, which is asymptotically self-similar in the space-time, illustrates how the cage effect confines each particle within a short radius on one hand and creates collective motion of numerous particles on the other hand. As the time elapses, the correlation length grows unlimitedly, and the generalized susceptibility based on the overlap density converges to a finite value which is an increasing function of the density. The distribution function behind these dynamical four-point correlations and its extension to three-dimensional cases, respecting the tensorial character of the two-particle displacement correlation, are also discussed.

Everlasting effect of initial conditions on single-file diffusion

We study the dynamics of a tagged particle in an environment of point Brownian particles with hard-core interactions in an infinite one-dimensional channel (a single-file model). In particular, we examine the influence of initial conditions on the dynamics of the tagged particle. We compare two initial conditions: equal distances between particles and uniform density distribution. The effect is shown by the differences of mean-square-displacement and correlation function for the two ensembles of initial conditions. We discuss the violation of Einstein relation, and its dependence on the initial condition, and the difference between time and ensemble averaging. More specifically, using the Jepsen line, we will discuss how transport coefficients, like diffusivity, depend on the initial state. Our work shows that initial conditions determine the long time limit of the dynamics, and in this sense the system never forgets its initial state in complete contrast with thermal systems (i.e., a closed system that attains equilibrium independent of the initial state).

Drift in Diffusion Gradients

The longstanding problem of Brownian transport in a heterogeneous quasi one-dimensional medium with space-dependent self-diffusion coefficient is addressed in the overdamped (zero mass) limit. A satisfactory mesoscopic description is obtained in the Langevin equation formalism by introducing an appropriate drift term, which depends on the system macroscopic observables, namely the diffuser concentration and current. The drift term is related to the microscopic properties of the medium. The paradoxical existence of a finite drift at zero current suggests the possibility of designing a Maxwell demon operating between two equilibrium reservoirs at the same temperature.

Single-file diffusion in periodic energy landscapes: the role of hydrodynamic interactions

We report on the dynamical properties of interacting colloids confined to one dimension and subjected to external periodic energy landscapes. We particularly focus on the influence of hydrodynamic interactions on the mean-square displacement. Using Brownian dynamics simulations, we study colloidal systems with two types of repulsive interparticle interactions, namely, Yukawa and superparamagnetic potentials. We find that in the homogeneous case, hydrodynamic interactions lead to an enhancement of the particle mobility and the mean-square displacement at long times scales as t(α), with α=1/2+ε and ε being a small correction. This correction, however, becomes much more important in the presence of an external field, which breaks the homogeneity of the particle distribution along the line and, therefore, promotes a richer dynamical scenario due to the hydrodynamical coupling among particles. We provide here the complete dynamical scenario in terms of the external potential parameters: amplitude and commensurability.

Diffusion in a quasi-one-dimensional system on a periodic substrate

The diffusion of charged particles interacting through a repulsive Yukawa potential, exp(-r/λ)/r, confined by a parabolic potential in the y direction and subjected to a periodic substrate potential in the x direction is investigated. Langevin dynamic simulations are used to investigate the effect of the particle density, the amplitude of the periodic substrate, and the range of the interparticle interaction potential on the diffusive behavior of the particles. We found that in general the diffusion is suppressed with increasing the amplitude of the periodic potential, but for specific values of the strength of the substrate potential a remarkable increase of the diffusion is found with increasing the periodic potential amplitude. In addition, we found a strong dependence of the diffusion on the specific arrangement of the particles, e.g., single-chain versus multichain configuration. For certain particle configurations, a reentrant behavior of the diffusion is found as a function of the substrate strength due to structural transitions in the ordering of the particles.

Single-file diffusion and kinetics of template-assisted assembly of colloids

We report computer simulation studies of the kinetics of ordering of a two-dimensional system of particles on a template with a one-dimensional periodic pattern. In equilibrium, one obtains a reentrant liquid-solid-liquid phase transition as the strength of the substrate potential is varied. We show that domains of crystalline order grow as ~t(1/z), with z~4, with a possible crossover to z~2 at late times. We argue that the t(1/4) law originates from single-file motion and annihilation of defect pairs of opposite topological charge along channels created by the template.

Ratcheting of driven attracting colloidal particles: temporal density oscillations and current multiplicity

We consider the unidirectional particle transport in a suspension of colloidal particles which interact with each other via a pair potential having a hard-core repulsion plus an attractive tail. The colloids are confined within a long narrow channel and are driven along by a dc or an ac external potential. In addition, the walls of the channel interact with the particles via a ratchetlike periodic potential. We use dynamical density functional theory to compute the average particle current. In the case of dc drive, we show that as the attraction strength between the colloids is increased beyond a critical value, the stationary density distribution of the particles loses its stability leading to depinning and a time-dependent density profile. Attraction induced symmetry breaking gives rise to the coexistence of stable stationary density profiles with different spatial periods and time-periodic density profiles, each characterized by different values for the particle current.

Effect of correlated noise on quasi-one-dimensional diffusion

Single-file diffusion (SFD) of an infinite one-dimensional chain of interacting particles has a long-time mean-square displacement ∝t(1/2), independent of the type of interparticle repulsive interaction. This behavior is also observed in finite-size chains, although only for certain intervals of time t depending on the chain length L, followed by the ∝t for t→∞, as we demonstrate for a closed circular chain of diffusing interacting particles. Here, we show that spatial correlation of noise slows down SFD and can result, depending on the amount of correlated noise, in either subdiffusive behavior ∝tα, where 0<α<1/2, or even in a total suppression of diffusion (in the limit N→∞). Spatial correlation can explain the subdiffusive behavior in recent SFD experiments in circular channels.

Collective shuttling of attracting particles in asymmetric narrow channels

The rectification of a single file of attracting particles subjected to a low frequency ac drive is proposed as a working mechanism for particle shuttling in an asymmetric narrow channel. Increasing the particle attraction results in the file condensing, as signaled by the dramatic enhancement of the net particle current. The magnitude and direction of the current become extremely sensitive to the actual size of the condensate, which can then be made to shuttle between two docking stations, transporting particles in one direction, with an efficiency much larger than conventional diffusive models predict.

Dynamics of heterogeneous hard spheres in a file

Normal dynamics in a quasi-one-dimensional channel of length L (→∞) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W∼D(-γ) for small D, where 0≤γ<1. The initial spheres' density ρ is nonuniform and scales with the distance (from the origin) l as ρ∼l(-α), 0≤α≤1. An approximation for the N-particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys <r2>∼t((1-γ)/(2c-γ)), where c=1/(1+α). The PDF of the tagged particle is gaussian in position. Generalizations of these results are considered.

Diffusion of tagged particle in an exclusion process

We study the diffusion of tagged hard-core interacting Brownian point particles under the influence of an external force field in one dimension. Using the Jepsen line we map this many-particle problem onto a single particle one. We obtain general equations for the distribution and the mean-square displacement <(xT)2> of the tagged center particle valid for rather general external force fields and initial conditions. The case of symmetric distribution of initial conditions around the initial position of the tagged particle on x=0 and symmetric potential fields V(x)=V(-x) yields zero drift <xT>=0 and is investigated in detail. We find <(xT)2>=R(1-R)/2Nr2 where 2N is the (large) number of particles in the system. R is a single particle reflection coefficient, i.e., the probability that a particle free of collisions starts on x0>0 and remains in x>0 while r is the probability density of noninteracting particles on the origin. We show that this equation is related to the mathematical theory of order statistics and it can be used to find <(xT)2> even when the motion between collision events is not Brownian (e.g., it might be ballistic or anomalous diffusion). As an example we derive the Percus relation for non-Gaussian diffusion. A wide range of physical behaviors emerge which are very different than the classical single file subdiffusion <(xT)2> approximately t1/2 found for uniformly distributed particles in an infinite space and in the absence of force fields.

Dynamics of colloids in a narrow channel driven by a nonuniform force

Using Brownian dynamics simulations, we investigate the dynamics of colloids confined in two-dimensional narrow channels driven by a nonuniform force Fdr(y) . We considered linear-gradient, parabolic, and deltalike driving-force profiles. This driving force induces melting of the colloidal solid (i.e., shear-induced melting), and the colloidal motion experiences a transition from elastic to plastic regime with increasing Fdr. For intermediate Fdr (i.e., in the transition region) the response of the system, i.e., the distribution of the velocities of the colloidal chains upsiloni(y) , in general does not coincide with the profile of the driving force Fdr(y), and depends on the magnitude of Fdr, the width of the channel, and the density of colloids. For example, we show that the onset of plasticity is first observed near the boundaries while the motion in the central region is elastic. This is explained by: (i) (in)commensurability between the chains due to the larger density of colloids near the boundaries, and (ii) the gradient in Fdr. Our study provides a deeper understanding of the dynamics of colloids in channels and could be accessed in experiments on colloids (or in dusty plasma) with, e.g., asymmetric channels or in the presence of a gradient potential field.

Theory of single file diffusion in a force field

The dynamics of hard-core interacting Brownian particles in an external potential field is studied in one dimension. Using the Jepsen line we find a very general and simple formula relating the motion of the tagged center particle, with the classical, time dependent single particle reflection R and transmission T coefficients. Our formula describes rich physical behaviors both in equilibrium and the approach to equilibrium of this many body problem.

Effects of self-assembly on diffusion mechanisms of triblock copolymers in aqueous solution

Molecular dynamics of self-assembling triblock copolymers in a mixture with water was explored using nuclear magnetic resonance (NMR) diffusometry with high-intensity field gradient pulses. With varying concentration, the diffusivities are found to cover 4 orders of magnitude. The dramatic changes in both the rates and patterns of polymer propagation can be attributed to their ordering in supermolecular formations and prove to be a sensitive means for probing structural and dynamic features of self-aggregation which only now, owing to recent progress in NMR diffusometry, have become accessible to direct observation.

Langevin formulation for single-file diffusion

We introduce a stochastic equation for the microscopic motion of a tagged particle in the single-file model. This equation provides a compact representation of several of the system's properties such as fluctuation-dissipation and linear-response relations, achieved by means of a diffusion noise approach. Most importantly, the proposed Langevin equation reproduces quantitatively the three temporal regimes and the corresponding time scales: ballistic, diffusive, and subdiffusive.

Superparamagnetic colloids confined in narrow corrugated substrates

We report a Brownian dynamics simulation study of the structure and dynamics of superparamagnetic colloids subject to external substrate potentials and confined in narrow channels. Our study is motivated by the importance of phenomena like commensurable-incommensurable phase transitions, anomalous diffusion, and stochastic activation processes that are closely related to the system under investigation. We focus mainly on the role of the substrate in the order-disorder mechanisms that lead to a rich variety of commensurate and incommensurate phases, as well as its effect on the single-file diffusion in interacting systems and the depinning transition in one dimension.

Deterministic single-file dynamics in collisional representation

We re-examine numerically the diffusion of a deterministic, or ballistic single file with preassigned velocity distribution (Jepsen's gas) from a collisional viewpoint. For a two-modal velocity distribution, where half the particles have velocity +/-c, the collisional statistics is analytically proven to reproduce the continuous time representation. For a three-modal velocity distribution with equal fractions, where less than 12 of the particles have velocity +/-c, with the remaining particles at rest, the collisional process is shown to be inhomogeneous; its stationary properties are discussed here by combining exact and phenomenological arguments. Collisional memory effects are then related to the negative power-law tails in the velocity autocorrelation functions, predicted earlier in the continuous time formalism. Numerical and analytical results for Gaussian and four-modal Jepsen's gases are also reported for the sake of a comparison.

Stretched Markov nature of single-file self-dynamics

We study the generalized diffusion of a tagged particle in a one-dimensional fluid of hard-point particles. The dynamics of a single particle in its nonuniform, nondeterministic environment is assumed known. On eliminating suitably defined transients from the exact solution, we find a universal form for the tagged particle dynamics when written in terms of stretched space and time, appearing as the classical telegrapher's equation.

Numerical method for solving stochastic differential equations with Poissonian white shot noise

We propose a numerical integration scheme to solve stochastic differential equations driven by Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches the Euler formula if the Poissonian noise approaches the Gaussian white noise. The accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by Poissonian white shot noise in a spatially periodic potential. We find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the Poissonian white shot noise; this holds true even if the limit of Gaussian white noise is approached.

Transport of a heated granular gas in a washboard potential

We study numerically the motion of a one dimensional array of Brownian particles in a washboard potential, driven by an external stochastic force and interacting via short range repulsive forces. In particular, we investigate the role of instantaneous elastic and inelastic collisions on the system dynamics and transport. The system displays a locked regime, where particles may move only via activated processes and a running regime where particles drift along the direction of the applied field. By tuning the value of the friction parameter controlling the Brownian motion we explore both the overdamped dynamics and the underdamped dynamics. In the two regimes we considered the mobility and the diffusivity of the system as functions of the tilt and other relevant control parameters such as coefficient of restitution, particle size, and total number of particles. We find that while in the overdamped regime the results for the interacting systems present similarities with the known noninteracting case, in the underdamped regime the inelastic collisions determine a rich variety of behaviors among which is an unexpected enhancement of the inelastic diffusion.

Collisional statistics of a stochastic single file

The anomalous diffusion of a single file of Brownian particles moving on a circle at a given temperature is characterized in terms of nearest-neighbor collisions. The time and the distance a particle diffuses (normally) between two successive collisions are computed numerically; their means, distributions, and correlation functions are determined for different values of the file parameters and reproduced analytically by means of simple phenomenological arguments. Most notably, the jump autocorrelation functions develop slow power-law tails. The ensuing impact representation of the single file dynamics suggests an alternate description of the single file diffusion as a geometrically constrained fluctuation mechanism.

Fractional diffusion interpretation of simulated single-file systems in microporous materials

The single-file diffusion of water in the straight channels of two different crystalline microporous aluminosilicates (zeolites bikitaite and Li-ABW) was studied by comparing the results of molecular dynamics computer simulations with the predictions of anomalous diffusion theory modeled by using fractional diffusion equations. At high coverage, the agreement is reasonably good, in particular for sufficiently large displacements and sufficiently long times. At low coverage, interesting phenomena appear in the simulation results, such as multimodal propagators, which could be interpreted on the basis of fractional Fokker-Planck equations. The results are discussed also in view of different theories that have been proposed to model the single-file diffusion process.

Determination of the nonlinear dielectric increment in the Cole-Davidson model

The problem of the nonlinear dielectric relaxation of complex liquids is tackled in the context of the Cole-Davidson [J. Chem. Phys. 19, 1484 (1951)] model. By using an appropriate time derivative of noninteger order, an infinite hierarchy of differential-recurrence relations for the moments (expectation values of the Legendre polynomials) is obtained. The solution is established for the stationary regime of an ensemble of polar and symmetric-top molecules acted on by a strong dc bias electric field superimposed on a weak ac electric field. The results for the first three nonlinear harmonic components of the electric susceptibility are analytically established and illustrated with the help of Argand diagrams for the nonlinear dielectric increment and three-dimensional dispersion and absorption spectra for the second and the third harmonic components as a function of the anomalous exponent beta</=1, the value of which gives rise to skewed arcs (Argand plots) and asymmetric shapes (loss spectra) in the high-frequency domain.

Subdiffusion and long-time anticorrelations in a stochastic single file

The subdiffusion of a stochastic single file is interpreted as a jumping process. Contrary to the current continuous time random walk models, its statistics is characterized by finite averages of the jumping times and square displacements. Subdiffusion is then related to a persistent anticorrelation of the jump sequences. In continuous time representation, this corresponds to negative power-law velocity autocorrelations, attributable to the restricted geometry of the file diffusion.

Diffusion of interacting Brownian particles: Jamming and anomalous diffusion

The free self-diffusion of an assembly of interacting particles confined on a quasi-one-dimensional ring is investigated both numerically and analytically. The interparticle pairwise interaction can be either attractive or repulsive and the energy barrier opposing thermal hopping of two particles one past the other is finite. Thus, for sufficiently long times, self-diffusion becomes normal or conventional diffusion. However, depending on the particle density, subdiffusive transients with exponent 12 and suppression of normal diffusion are observed. Above a certain density threshold, a sudden drop to zero of the diffusion coefficient for attractive particles signals the transition to a jammed phase. Furthermore, a Gaussian cluster of attractive particles condenses, by shrinking in size, for densities larger than such density threshold; lower density clusters spread out, regardless of the interaction sign, through a diffusion mechanism that is anomalous at short times, and normal for sufficiently long times. These effects could be observed in systems with colloidal particles, vortices, electrons, among other interacting particle systems.