arXiv subjects

Igor M. Sokolov

Publications and source records attributed to Igor M. Sokolov.

At least 73 records · Page 4Linked to original sources

arXiv2014

Model of lateral diffusion in ultrathin layered films

We consider the diffusion of markers in a layered medium, with the lateral diffusion coefficient being the function of hight. We show that the probability density of the lateral displacements follows one-dimensional Batchelor's equation with time-dependent diffusion coefficient governed by the particles' redistribution in height. For the film of a finite thickness the resulting mean squared displacement exhibits superdiffusion at short times and crosses over to normal diffusion at long times. The approach is used for description of experimental results on inhomogeneous molecular diffusion in thin liquid films deposited on solid surfaces.

cond-mat.mes-hall↗

arXiv2014

Tracer diffusion inside fibrinogen layers

We investigate the obstructed motion of tracer (test) particles in crowded environments by carrying simulations of two-dimensional Gaussian random walk in model fibrinogen monolayers of different orientational ordering. The fibrinogen molecules are significantly anisotropic and therefore they can form structures where orientational ordering, similar to the one observed in nematic liquid crystals, appears. The work focuses on the dependence between level of the orientational order (degree of environmental crowding) of fibrinogen molecules inside a layer and non-Fickian character of the diffusion process of spherical tracer particles moving within the domain. It is shown that in general particles motion is subdiffusive and strongly anisotropic, and its characteristic features significantly change with the orientational order parameter, concentration of fibrinogens and radius of a diffusing probe.

physics.chem-ph↗

arXiv2014

Absence of Anderson localization of light in a random ensemble of point scatterers

As discovered by Philip Anderson in 1958, strong disorder can block propagation of waves and lead to the localization of wave-like excitations in space. Anderson localization of light is particularly exciting in view of its possible applications for random lasing or quantum information processing. We show that, surprisingly, Anderson localization of light cannot be achieved in a random three-dimensional ensemble of point scattering centers that is the simplest and widespread model to study the multiple scattering of waves. Localization is recovered if the vector character of light is neglected. This shows that, at least for point scatterers, the polarization of light plays an important role in the Anderson localization problem.

physics.optics↗

arXiv2013

Weak ergodicity breaking in an anomalous diffusion process of mixed origins

The ergodicity breaking parameter is a measure for the heterogeneity among different trajectories of one ensemble. In this report this parameter is calculated for fractional Brownian motion with a random change of time scale, often called "subordination". We proceed to show that this quantity is the same as the known CTRW case.

physics.data-an↗

arXiv2013

Scaled Brownian motion as a mean field model for continuous time random walks

We consider scaled Brownian motion (sBm), a random process described by a diffusion equation with explicitly time-dependent diffusion coefficient $D(t) = D_0 t^{α- 1}$ (Batchelor's equation) which, for $α< 1$, is often used for fitting experimental data for subdiffusion of unclear genesis. We show that this process is a close relative of subdiffusive continuous-time random walks and describes the motion of the center of mass of a cloud of independent walkers. It shares with subdiffusive CTRW its non-stationary and non-ergodic properties. The non-ergodicity of sBm does not however go hand in hand with strong difference between its different realizations: its heterogeneity ("ergodicity breaking") parameter tends to zero for long trajectories.

physics.data-an↗

arXiv2013

Disentangling sources of anomalous diffusion

We show that some important properties of subbdiffusion of unknown origin (including those of mixed origin) can be easily assessed when findeng the "fundamental moment" of the corresponding process, i.e., the one which is additive in time. In subordinated processes, the index of the fundamental moment is inherited from the parent process and its time-dependence from the leading one. In models of particle's motion in disordered potentials, the index is governed by the structural part of the disorder while the time dependence is given by its energetic part.

physics.data-an↗

arXiv2012

Diffusion of small particles in a solid polymeric medium

We analyze diffusion of small particles in a solid polymeric medium taking into account a short range particle-polymer interaction. The system is modeled by a particle diffusion on a ternary lattice where the sites occupied by polymer segments are blocked, the ones forming the hull of the chains correspond to the places at which the interaction takes place, and the rest are voids, in which the diffusion is free. In the absence of interaction the diffusion coefficient shows only a weak dependence on the polymer chain length and its behavior strongly resembles usual site percolation. In presence of interactions the diffusion coefficient (and especially its temperature dependence) shows a non-trivial behavior depending on the sign of interaction and on whether the voids and the hulls of the chains percolate or not. The temperature dependence may be Arrhenius-like or strongly non-Arrhenius, depending on parameters. The analytical results obtained within the effective medium approximation are in qualitative agreement with those of Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2012

A Test for Determining a Subdiffusive Model in Ergodic Systems from Single Trajectories

Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading to continuous-time random walks) can easily be distinguished from the rest by testing their non-ergodicity, the latter two cases are harder to distinguish. We propose a statistical test for distinguishing between these two based on the space-filling properties of trajectories, and prove its feasibility and specificity using synthetic data. We moreover present a flow-chart for making a decision on a type of subdiffusion for a broader class of models.

cond-mat.dis-nn↗

arXiv2012

Active Particles Forced by an Asymmetric Dichotomous Angle Drive

We analyze the dynamics of particles in two dimensions with constant speed and a stochastic switching angle dynamics defined by a correlated dichotomous Markov process (telegraph noise) plus Gaussian white noise. We study various cases of the asymptotic diffusional motion of the particle which is characterized by the effective diffusion coefficient. Expressions for this coefficient are derived and discussed in dependence on the correlation time and the intensity of the noise. The situation with a given mean curvature is of special interest since a non-monotonic behavior of the effective diffusion coefficient as function of the noise intensity and correlation time is found. A timescale matching condition for maximal diffusion is formulated.

cond-mat.stat-mech↗

arXiv2012

Normal and anomalous diffusion in random potential landscapes

A relation between the effective diffusion coefficient in a lattice with random site energies and random trasition rates and the macroscopic conductivity in a random resistor network allows for elucidating possible sources of anomalous diffusion in random potential models. We show that subdiffusion is only possible either if the mean Boltzmann factor in the corresponding potential diverges or if the percolation concentration in the system is equal to unity (or both), and that superdiffusion is impossible in our system under any condition. We show also other useful applications of this relation.

cond-mat.stat-mech↗

arXiv2012

Bulk-mediated diffusion on a planar surface: full solution

We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random walk approach we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover we study the long-time dynamics for the surface motion.

cond-mat.stat-mech↗

arXiv2012

Impact of inertia on biased Brownian transport in confined geometries

We consider the impact of inertia on biased Brownian motion of point particles in a two-dimensional channel with sinusoidally varying width. If the time scales of the problem separate, the adiabatic elimination of the transverse degrees of freedom leads to an effective description for the motion along the channel given by the potential of mean force. The possibility of such description is intimately connected with equipartition. Numerical simulations show that in the presence of external bias the equipartition may break down leading to non-monotonic dependence of mobility on external force and several other interesting effects.

cond-mat.stat-mech↗

arXiv2011

The Unequal Twins - Probability Distributions Aren't Everything

It is the common lore to assume that knowing the equation for the probability distribution function (PDF) of a stochastic model as a function of time tells the whole picture defining all other characteristics of the model. We show that this is not the case by comparing two exactly solvable models of anomalous diffusion due to geometric constraints: The comb model and the random walk on a random walk (RWRW). We show that though the two models have exactly the same PDFs, they differ in other respects, like their first passage time (FPT) distributions, their autocorrelation functions and their aging properties.

cond-mat.stat-mech↗

arXiv2011

Harmonic oscillator under Levy noise: Unexpected properties in the phase space

A harmonic oscillator under influence of the noise is a basic model of various physical phenomena. Under Gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to the bivariate Gaussian distribution with elliptic level lines. The distribution of phase is homogeneous. None of these properties hold in the general Lévy case. Thus, the level lines of the joint probability density are not elliptic. The coordinate and the velocity of the oscillator are strongly dependent, and this dependence is quantified by introducing the corresponding parameter ("width deficit"). The distribution of the phase is inhomogeneous and highly nontrivial.

cond-mat.stat-mech↗

arXiv2011

Effective surface motion on a reactive cylinder of particles that perform intermittent bulk diffusion

In many biological and small scale technological applications particles may transiently bind to a cylindrical surface. In between two binding events the particles diffuse in the bulk, thus producing an effective translation on the cylinder surface. We here derive the effective motion on the surface, allowing for additional diffusion on the cylinder surface itself. We find explicit solutions for the number of adsorbed particles at one given instant, the effective surface displacement, as well as the surface propagator. In particular sub- and superdiffusive regimes are found, as well as an effective stalling of diffusion visible as a plateau in the mean squared displacement. We also investigate the corresponding first passage and first return problems.

cond-mat.stat-mech↗

arXiv2010

Lévy Ratchet in a Weak Noise Limit: Theory and Simulation

We study the motion of a particle embedded in a time independent periodic potential with broken mirror symmetry and subjected to a Lévy noise possessing Lévy stable probability law (Lévy ratchet). We develop analytical approach to the problem based on the asymptotic probabilistic method of decomposition proposed by P. Imkeller and I. Pavlyukevich [J. Phys. A {\bf39}, L237 (2006); Stoch. Proc. Appl. {\bf116}, 611 (2006)]. We derive analytical expressions for the quantities characterizing the particle motion, namely the splitting probabilities of first escape from a single well, the transition probabilities and the particle current. A particular attention is devoted to the interplay between the asymmetry of the ratchet potential and the asymmetry (skewness) of the Lévy noise. Intensive numerical simulations demonstrate a good agreement with the analytical predictions for sufficiently small intensities of the Lévy noise driving the particle.

cond-mat.stat-mech↗

arXiv2010

Quantum memory for light via stimulated off-resonant Raman process: beyond the three-level Lambda-scheme approximation

We consider a quantum memory scheme based on the conversion of a signal pulse into a long-lived spin coherence via stimulated off-resonant Raman process. For a storing medium consisting of alkali atoms, we have calculated the Autler-Townes resonance structure created by a strong control field. By taking into account the upper hyperfine states of the D1 optical transition, we show important deviations from the predictions of the usual three-level Lambda-scheme approximation and we demonstrate an enhancement of the process for particular detunings of the control. We estimate the memory efficiency one can obtain using this configuration.

quant-ph↗

arXiv2010

Stationary states in single-well potentials under symmetric Levy noises

We discuss the existence of stationary states for subharmonic potentials $V(x) \propto |x|^c$, $c<2$, under action of symmetric $α$-stable noises. We show analytically that the necessary condition for the existence of the steady state is $c>2-α$. These states are characterized by heavy-tailed probability density functions which decay as $P(x) \propto x^{-(c+α-1)}$ for $|x| \to \infty$, i.e. stationary states posses a heavier tail than the corresponding $α$-stable law. Monte Carlo simulations confirm the existence of such stationary states and the form of the tails of corresponding probability densities.

cond-mat.stat-mech↗