arXiv subjects

I. M. Sokolov

Publications and source records attributed to I. M. Sokolov.

At least 91 records · Page 5Linked to original sources

arXiv2007

Multi-point Distribution Function for the Continuous Time Random Walk

We derive an explicit expression for the Fourier-Laplace transform of the two-point distribution function $p(x_1,t_1;x_2,t_2)$ of a continuous time random walk (CTRW), thus generalizing the result of Montroll and Weiss for the single point distribution function $p(x_1,t_1)$. The multi-point distribution function has a structure of a convolution of the Montroll-Weiss CTRW and the aging CTRW single point distribution functions. The correlation function $ $ for the biased CTRW process is found. The random walk foundation of the multi-time-space fractional diffusion equation [Baule and Friedrich [{\em Europhysics Letters} {\bf 77} 10002 (2007)] is investigated using the unbiased CTRW in the continuum limit.

cond-mat.stat-mech↗

arXiv2007

Finite size effects in Barabasi-Albert growing networks

We investigate the influence of the network's size on the degree distribution in Barabasi-Albert model of growing network with initial attractiveness. Our approach based on spectral moments allows to treat analytically several variants of the model and to calculate the cut-off function giving finite size corrections to the degree distribution. We study the effect of initial configuration as well as of addition more than one link per time step. The results indicate that asymptotic properties of the cut-off depend only on the exponent in the power law describing the tail of the degree distribution.

cond-mat.stat-mech↗

arXiv2006

Growing networks under geographical constraints

Inspired by the structure of technological networks, we discuss network evolution mechanisms which give rise to topological properties found in real spatial networks. Thus, the peculiar structure of transport and distribution networks is fundamentally determined by two factors. These are the dependence of the spatial interaction range of vertices on the vertex attractiveness (or importance within the network) and on the inhomogeneous distribution of vertices in space. We propose and analyse numerically a simple model based on these generating mechanisms which seems, for instance, to be able to reproduce known structural features of the Internet.

physics.soc-ph↗

arXiv2006

Dispersionless transport in a washboard potential

We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.

cond-mat.stat-mech↗

arXiv2006

Mesoscopic description of reactions under anomalous diffusion: A case study

Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant concentrations separate. In the present work we discuss the possibilities of a generalization of reaction-diffusion equations to the case of anomalous diffusion described by continuous-time random walks with decoupled step length and waiting time probability densities, the first being Gaussian or Levy, the second one being an exponential or a power-law lacking the first moment. We consider a special case of an irreversible or reversible A ->B conversion and show that only in the Markovian case of an exponential waiting time distribution the diffusion- and the reaction-term can be decoupled. In all other cases, the properties of the reaction affect the transport operator, so that the form of the corresponding reaction-anomalous diffusion equations does not closely follow the form of the usual reaction-diffusion equations.

cond-mat.stat-mech↗

arXiv2006

Death of linear response and field-induced dispersion in subdiffusion

We discuss the response of continuous time random walks to an oscillating external field within the generalized master equation approach. We concentrate on the time dependence of the two first moments of the walker's displacements. We show that for power law waiting time distributions with 0 < alpha < 1 corresponding to a semi-Markovian situation showing nonstationarity the mean particle position tends to a constant, and the response to the external perturbation dies out. On the other hand, the oscillating field leads to a new additional contribution to the dispersion of the particle position, proportional to the square of its amplitude and growing with time. These new effects, amenable to experimental observation, result directly from the non-stationary property of the system.

cond-mat.stat-mech↗

arXiv2006

Diffuse light scattering dynamics under conditions of electromagnetically induced transparency

We show that, under conditions of electromagnetically induced transparency (EIT), a significant portion of the incident probe pulse can be transferred into Rayleigh and Raman scattering channels. The light scattered into the Rayleigh channel emerges from the sample with an EIT time delay. We show that a proper description of the probe light propagation in the sample should include, in the diffusion dynamics, a spin polariton generated by the two-photon EIT process. The results have important implications for studies of weak light localization, and for manipulation of single and few photon states in ultracold atomic gases.

physics.atom-ph↗

arXiv2005

First Passage Time Densities in Resonate-and-Fire Models

Motivated by the dynamics of resonant neurons we discuss the properties of the first passage time (FPT) densities for nonmarkovian differentiable random processes. We start from an exact expression for the FPT density in terms of an infinite series of integrals over joint densities of level crossings, and consider different approximations based on truncation or on approximate summation of this series. Thus, the first few terms of the series give good approximations for the FPT density on short times. For rapidly decaying correlations the decoupling approximations perform well in the whole time domain. As an example we consider resonate-and-fire neurons representing stochastic underdamped or moderately damped harmonic oscillators driven by white Gaussian or by Ornstein-Uhlenbeck noise. We show, that approximations reproduce all qualitatively different structures of the FPT densities: from monomodal to multimodal densities with decaying peaks. The approximations work for the systems of whatever dimension and are especially effective for the processes with narrow spectral density, exactly when markovian approximations fail.

physics.data-an↗

arXiv2005

First Passage Time Densities in Non-Markovian Models with Subthreshold Oscillations

Motivated by the dynamics of resonant neurons we consider a differentiable, non-Markovian random process $x(t)$ and particularly the time after which it will reach a certain level $x_b$. The probability density of this first passage time is expressed as infinite series of integrals over joint probability densities of $x$ and its velocity $\dot{x}$. Approximating higher order terms of this series through the lower order ones leads to closed expressions in the cases of vanishing and moderate correlations between subsequent crossings of $x_b$. For a linear oscillator driven by white or coloured Gaussian noise, which models a resonant neuron, we show that these approximations reproduce the complex structures of the first passage time densities characteristic for the underdamped dynamics, where Markovian approximations (giving monotonous first passage time distribution) fail.

cond-mat.stat-mech↗

arXiv2005

On reaction-subdiffusion equations

To analyze possible generalizations of reaction-diffusion schemes for the case of subdiffusion we discuss a simple monomolecular conversion A --> B. We derive the corresponding kinetic equations for local A and B concentrations. Their form is rather unusual: The parameters of reaction influence the diffusion term in the equation for a component A, a consequence of the nonmarkovian nature of subdiffusion. The equation for a product contains a term which depends on the concentration of A at all previous times. Our discussion shows that reaction-subdiffusion equations may not resemble the corresponding reaction-diffusion ones and are not obtained by a trivial change of the diffusion operator for a subdiffusion one.

cond-mat.stat-mech↗

arXiv2005

Spectra and waiting-time densities in firing resonant and nonresonant neurons

The response of a neural cell to an external stimulus can follow one of the two patterns: Nonresonant neurons monotonously relax to the resting state after excitation while resonant ones show subthreshold oscillations. We investigate how do these subthreshold properties of neurons affect their suprathreshold response. Vice versa we ask: Can we distinguish between both types of neuronal dynamics using suprathreshold spike trains? The dynamics of neurons is given by stochastic FitzHugh-Nagumo and Morris-Lecar models with either having a focus or a node as the stable fixpoint. We determine numerically the spectral power density as well as the interspike interval density in response to a random (noise-like) signals. We show that the information about the type of dynamics obtained from power spectra is of limited validity. In contrast, the interspike interval density gives a very sensitive instrument for the diagnostics of whether the dynamics has resonant or nonresonant properties. For the latter value we formulate a fit formula and use it to reconstruct theoretically the spectral power density, which coincides with the numerically obtained spectra. We underline that the renewal theory is applicable to analysis of suprathreshold responses even of resonant neurons.

q-bio.NC↗

arXiv2005

Multimode entanglement of light and atomic ensembles via off-resonant coherent forward scattering

Quantum theoretical treatment of coherent forward scattering of light in a polarized atomic ensemble with an arbitrary angular momentum is developed. We consider coherent forward scattering of a weak radiation field interacting with a realistic multi-level atomic transition. Based on the concept of an effective Hamiltonian and on the Heisenberg formalism, we discuss the coupled dynamics of the quantum fluctuations of the polarization Stokes components of propagating light and of the collective spin fluctuations of the scattering atoms. We show that in the process of coherent forward scattering this dynamics can be described in terms of a polariton-type spin wave created in the atomic sample. Our work presents a general example of entangling process in the system of collective quantum states of light and atomic angular momenta, previously considered only for the case of spin-1/2 atoms. We use the developed general formalism to test the applicability of spin-1/2 approximation for modelling the quantum non-demolishing measurement of atoms with a higher angular momentum.

quant-ph↗

arXiv2004

From Diffusion to Anomalous Diffusion: A Century after Einstein's Brownian Motion

Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term memory. The coarse-grained behavior of such processes is described by the diffusion equation. However, many natural processes do not possess the Markovian property and exhibit to anomalous diffusion. We consider here the case of subdiffusive processes, which are semi-Markovian and correspond to continuous-time random walks in which the waiting time for a step is given by a probability distribution with a diverging mean value. Such a process can be considered as a process subordinated to normal diffusion under operational time which depends on this pathological waiting-time distribution. We derive two different but equivalent forms of kinetic equations, which reduce to know fractional diffusion or Fokker-Planck equations for waiting-time distributions following a power-law. For waiting time distributions which are not pure power laws one or the other form of the kinetic equation is advantageous, depending on whether the process slows down or accelerates in the course of time.

cond-mat.stat-mech↗

arXiv2004

From subdiffusion to superdiffusion of particles on solid surfaces

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.

cond-mat.stat-mech↗

arXiv2004

Steady-State Luminescence of Polymers: Effects of Flow and of Hydrodynamic Interactions

We consider a simple model for steady-state luminescence of single polymer chains in a dilute solution in the case when excitation quenching is due to energy transfer between a donor and an acceptor attached to the ends of the chain. We present numerical results for Rouse chains without or with hydrodynamic interactions, which are taken into account in a perturbative manner. We consider the situations of a quiescent solvent as well as the chain in a shear flow and discuss the dependence of the steady-state luminescence intensity on the strength of hydrodynamic interaction and on the shear rate in the flow.

cond-mat.soft↗

arXiv2004

Antilocalization in Coherent Backscattering of Light in a Multi-Resonance Atomic System

Theoretical prediction of antilocalization of light in ultracold atomic gas samples, in the weak localization regime, is reported. Calculations and Monte-Carlo simulations show that, for selected spectral ranges in the vicinity of atomic 85Rb hyperfine transitions, quantum coherence in optical transitions through nondegenerate hyperfine levels in multiple light scattering generates destructive interference in otherwise reciprocal scattering paths. This effect leads to enhancement factors less than unity in a coherent backscattering geometry, and suggests the possibility of enhanced diffusion of light in ultracold atomic vapors.

quant-ph↗

arXiv2004

Construction and properties of assortative random networks

Many social networks exhibit assortative mixing so that the predictions of uncorrelated models might be inadequate. To analyze the role of assortativity we introduce an algorithm which changes correlations in a network and produces assortative mixing to a desired degree. This degree is governed by one parameter p. Changing this parameter one can construct networks ranging from fully random (p = 0) to totally assortative (p = 1). We apply the algorithm to a Barabasi-Albert scale-free network and show that the degree of assortativity is an important parameter governing geometrical and transport properties of networks. Thus, the diameter of the network and the clustering coefficient increase dramatically with the degree of assortativity. Moreover, the concentration dependences of the size of the giant component in the node percolation problem for uncorrelated and assortative networks are strongly different.

cond-mat.stat-mech↗

arXiv2004

Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals

We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.

nlin.CD↗