arXiv subjects

Aleksei V. Chechkin

Publications and source records attributed to Aleksei V. Chechkin.

At least 19 recordsLinked to original sources

arXiv2026

Drift-diffusion interplay in active Brownian particles under orienting field

Magnetic active particles offer a versatile route to externally controlled microscale transport by combining self-propulsion with field-tunable orientation, as realized in both synthetic and living magnetic microswimmers. Here, we develop a theoretical framework for three-dimensional active Brownian motion in a uniform magnetic field, incorporating coupled translational and rotational dynamics and providing analytical approximations for low-order displacement moments. At long times, the system dynamics reduces to a combination of enhanced diffusion and permanent drift absent in regular active Brownian particles. The field acts as an external controller, channeling activity toward one of these two types of motion. At intermediate time scales, the interplay between rotational noise, self-propulsion, and magnetic alignment results in pronounced non-Gaussian displacement statistics. First-passage properties exhibit strong field sensitivity, highlighting the potential of magnetic guidance to optimize search processes and targeted delivery in active matter systems. Theoretical predictions are validated by numerical simulations.

cond-mat.soft↗

arXiv2026

Stochastic Dynamics of Domain Wall on a Racetrack: Impact of Line-Edge Roughness

We investigate the impact of line-edge roughness on current-driven domain wall dynamics in ferromagnetic racetracks. Modeling the edge disorder as a spatially correlated Ornstein-Uhlenbeck process, we demonstrate that even minimal experimentally relevant roughness induces pronounced stochastic pinning of domain walls. Notably, this stochasticity of the current-driven motion arises purely from spatial disorder, even in the absence of thermal fluctuations. The probability of a domain wall to reach a given position exhibits a robust sigmoidal dependence on the applied current, reflecting an effective distribution of depinning thresholds. At the same time, the underlying dynamics is highly nontrivial: the mean velocity exhibits a nonlinear dependence on both time and current, while the mean-square displacement exhibits a ballistic regime at short times followed by saturation due to trapping at pinning sites. These results demonstrate that line-edge roughness provides a controllable source of stochasticity and enables p-bit-like functionality in racetrack systems, offering a pathway toward hardware implementations of probabilistic and neuromorphic computing.

cond-mat.dis-nn↗

arXiv2026

Stochastic Dynamics of Skyrmions on a Racetrack: Impact of Equilibrium and Nonequilibrium Noise

Current-driven motion of domain walls and skyrmions is central to the operation of non-volatile magnetic memory devices. Racetrack memory requires current densities high enough to generate velocities above 50 m/s, but such conditions also enhance spin-current noise. We develop a theoretical framework based on the stochastic Thiele equation to analyze the effects of equilibrium (thermal) and nonequilibrium (spin-current) fluctuations on skyrmion dynamics. From this approach, we derive diffusion coefficients and mean-squared displacements that quantify stochastic motion under both noise sources. Micromagnetic simulations and analytical results demonstrate that spin-current noise dominates skyrmion dynamics in typical racetrack structures up to room temperature. We further address the first-passage-time problem, obtaining the mean first-passage time and its standard deviation along and across the racetrack. These results quantify how random displacements affect skyrmion propagation and detection, providing insights into error sources in high-speed racetrack memory devices.

cond-mat.dis-nn↗

arXiv2025

Different behaviors of diffusing diffusivity dynamics based on three different definitions of fractional Brownian motion

The effects of a "diffusing diffusivity" (DD), a stochastically time-varying diffusion coefficient, are explored within the frameworks of three different forms of fractional Brownian motion (FBM): (i) the Langevin equation driven by fractional Gaussian noise (LE-FBM), (ii) the Weyl integral representation introduced by Mandelbrot and van Ness (MN-FBM), and (iii) the Riemann-Liouville fractional integral representation (RL-FBM) due to L{é}vy. The statistical properties of the three FBM-generalized DD models are examined, including the mean-squared displacement (MSD), mean-squared increment (MSI), autocovariance function (ACVF) of increments, and the probability density function (PDF). Despite the long-believed equivalence of MN-FBM and LE-FBM, their corresponding FBM-DD models exhibit distinct behavior in terms of the MSD and MSI. In the MN-FBM-DD model, the statistical characteristics directly reflect an effective diffusivity equal to its mean value. In contrast, in LE-FBM-DD, correlations in the random diffusivity give rise to an unexpected crossover behavior in both MSD and MSI. We also find that the MSI and ACVF are nonstationary in RL-FBM-DD but stationary in the other two DD models. All DD models display a crossover from a short-time non-Gaussian PDF to a long-time Gaussian PDF. Our findings offer guidance for experimentalists in selecting appropriate FBM-generalized models to describe viscoelastic yet non-Gaussian dynamics in bio- and soft-matter systems with heterogeneous environments.

cond-mat.stat-mech↗

arXiv2024

Paradoxical non-Gaussian behavior in fractional Laplace motion with drift

We study fractional Laplace motion (FLM) obtained from subordination of fractional Brownian motion to a gamma process, in the presence of an external drift that acts on the composite process or of an internal drift acting solely on the parental process. We derive the statistical properties of this FLM process and find that the external drift does not influence the mean-squared displacement (MSD), whereas the internal drift leads to normal diffusion, dominating at long times in the subdiffusive Hurst exponent regime. We also investigate the intricate properties of the probability density function (PDF), demonstrating that it possesses a central Gaussian region, whose expansion in time is influenced by FBM's Hurst exponent. Outside of this region the PDF follows a non-Gaussian pattern. The kurtosis of this FLM process converges toward the Gaussian limit at long times insensitive to the extreme non-Gaussian tails. Additionally, in the presence of the external drift, the PDF remains symmetric and centered at $x=vt$. In contrast, for the internal drift this symmetry is broken. The results of our computer simulations are fully consistent with the theoretical predictions. The FLM model is suitable for describing stochastic processes with a non-Gaussian PDF and long-ranged correlations of the motion.

cond-mat.stat-mech↗

arXiv2024

Granular gases under resetting

We investigate the granular temperatures in force-free granular gases under exponential resetting. When a resetting event occurs, the granular temperature attains its initial value, whereas it decreases because of the inelastic collisions between the resetting events. We develop a theory and perform computer simulations for granular gas cooling in the presence of Poissonian resetting events. We also investigate the probability density function to quantify the distribution of granular temperatures. Our theory may help us to understand the behavior of nonperiodically driven granular systems.

cond-mat.soft↗

arXiv2023

Memory-multi-fractional Brownian motion with continuous correlations

We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent $α(t)$ in a changing environment. In MMFBM the built-in, long-range memory is continuously modulated by $α(t)$. We derive the essential statistical properties of MMFBM such as response function, mean-squared displacement (MSD), autocovariance function, and Gaussian distribution. In contrast to existing forms of FBM with time-varying memory exponents but reset memory structure, the instantaneous dynamic of MMFBM is influenced by the process history, e.g., we show that after a step-like change of $α(t)$ the scaling exponent of the MSD after the $α$-step may be determined by the value of $α(t)$ before the change. MMFBM is a versatile and useful process for correlated physical systems with non-equilibrium initial conditions in a changing environment.

cond-mat.stat-mech↗

arXiv2022

Non-Gaussian displacement distributions in models of heterogeneous active particle dynamics

We study the effect of randomly distributed diffusivities and speeds in two models for active particle dynamics with active and passive fluctuations. We demonstrate how non-Gaussian displacement distributions emerge in these models in the long time limit, including Cauchy-type and exponential (Laplace) shapes. Notably the resulting shapes of the displacement distributions with distributed diffusivities for the active models considered here are in striking contrast to passive diffusion models. For the active motion models our discussion points out the differences between active- and passive-noise. Specifically, we demonstrate that the case with active-noise is in nice agreement with measured data for the displacement distribution of social amoeba.

cond-mat.stat-mech↗

arXiv2022

Absence of confinement and non-Boltzmann stationary states of fractional Brownian motion in shallow external potentials

We study the diffusive motion of a particle in a subharmonic potential of the form $U(x)=|x|^c$ ($0 2(1-1/α)$ holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function (PDF). Moreover we discuss analogies of non-stationarity of L{é}vy flights in shallow external potentials.

cond-mat.stat-mech↗

arXiv2021

Complex diffusion-based kinetics of photoluminescence in semiconductor nanoplatelets

We present a diffusion-based simulation and theoretical models for explanation of photoluminescence (PL) emission intensity in semiconductor nanoplatelets. It is shown that the shape of PL intensity curves can be reproduced by the interplay of recombination, diffusion and trapping of excitons. The emission intensity at short times is purely exponential and is defined by recombination. At long times it is governed by the release of excitons from surface traps and is characterized by a power-law tail. We show that the crossover from one limit to another is controlled by diffusion properties. This intermediate region exhibits a rich behaviour depending on the value of diffusivity. Proposed approach reproduces all the features of experimental curves measured for different nanoplatelet systems.

cond-mat.mes-hall↗

arXiv2020

Lévy noise-driven escape from arctan potential wells

The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, L{é}vy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher-order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Lévy noise-driven escape from an almost rectangular, arctan potential well restricted by two absorbing boundaries. We unveil analogies of the observed transient dynamics to the general properties of stationary states of L{é}vy processes in single-well potentials. The first escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness and height, of the arctan potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.

cond-mat.stat-mech↗

arXiv2020

Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories

Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses spread or drugs may be delivered in biological cells. Similar time-series are being recorded of stock values in financial markets and of climate data. Such time-series are most typically evaluated in terms of time-average mean-squared displacements, which remain random variables for finite measurement times. Their statistical properties are different for different physical stochastic processes, thus allowing us to extract valuable information on the stochastic process itself. To exploit the full potential of the statistical information encoded in measured time-series we here propose an easy-to-implement and computationally inexpensive new methodology, based on deviations of the time-averaged mean-squared displacement from its ensemble average counterpart. Specifically, we use the upper bound of these deviations for Brownian motion to check the applicability of this approach to simulated and real data sets. By comparing the probability of deviations for different data sets, we demonstrate how the theoretical bound for Brownian motion reveals additional information about observed stochastic processes. We apply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracer beads measured in mucin hydrogels, and of geographic surface temperature anomalies. Our analysis shows how the large-deviation properties can be efficiently used as a simple yet effective routine test to reject the Brownian motion hypothesis and unveil crucial information on statistical properties such as ergodicity breaking and short-time correlations.

cond-mat.stat-mech↗

arXiv2020

Unexpected crossovers in correlated random-diffusivity processes

The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by "viscoelastic" anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the strong non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of "viscoelastic yet non-Gaussian" diffusion.

cond-mat.stat-mech↗

arXiv2019

First passage properties of asymmetric Lévy flights

Lévy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $α$-stable jump length distribution with long-tailed, power-law asymptote. As a result, the variance of Lévy Flights diverges and the trajectory is characterised by occasional extremely long jumps. Such long jumps significantly decrease the probability to revisit previous points of visitation, rendering Lévy Flights efficient search processes in one and two dimensions. To further quantify their precise property as random search strategies we here study the first-passage time properties of Lévy Flights in one-dimensional semi-infinite and bounded domains for symmetric and asymmetric jump length distributions. To obtain the full probability density function of first-passage times for these cases we employ two complementary methods. One approach is based on the space-fractional diffusion equation for the probability density function, from which the survival probability is obtained for different values of the stable index $α$ and the skewness (asymmetry) parameter $β$. The other approach is based on the stochastic Langevin equation with $α$-stable driving noise. Both methods have their advantages and disadvantages for explicit calculations and numerical evaluation, and the complementary approach involving both methods will be profitable for concrete applications. We also make use of the Skorokhod theorem for processes with independent increments and demonstrate that the numerical results are in good agreement with the analytical expressions for the probability density function of the first-passage times.

cond-mat.stat-mech↗

arXiv2019

Non-renewal resetting of scaled Brownian motion

We investigate an intermittent stochastic process, in which the diffusive motion with time-dependent diffusion coefficient $D(t)\sim t^{α-1}$, $α>0$ (scaled Brownian motion), is stochastically reset to its initial position and starts anew. The resetting follows a renewal process with either exponential or power-law distribution of the waiting times between successive renewals. The resetting events, however, do not affect the time dependence of the diffusion coefficient, so that the whole process appears to be a non-renewal one. We discuss the mean squared displacement of a particle and probability density function of its positions in such a process. We show that scaled Brownian motion with resetting demonstrates a rich behavior whose properties essentially depend on the interplay of the parameters of the resetting process and the particle's displacement in a free motion. The motion of particles can remain either almost unaffected by resetting, but can also get slowed down or even be completely suppressed. Especially interesting are the nonstationary situations in which the mean squared displacement stagnates but the distribution of positions does not tend to any steady state. \color{black} This behavior is compared to the situation (discussed in the other paper of this series) in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. We show that the properties of the probability densities in such processes (erazing or retaining the memory on the diffusion coefficient) are vastly different. \color{black}

cond-mat.stat-mech↗

arXiv2019

Scaled Brownian motion with renewal resetting

We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient $D(t) \sim t^{α-1}$ with $α> 0$ (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. \color{black} In the present work we discuss the situation, in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. The situation when the resetting of coordinate does not affect the diffusion coefficient's time dependence is considered in the other work of this series. We show that the properties of the probability densities in such processes (erazing or retaining the memory on the diffusion coefficient) are vastly different. \color{black} In addition we discuss the first passage properties of the scaled Brownian motion with renewal resetting and consider the dependence of the efficiency of search on the parameters of the process.

cond-mat.stat-mech↗

arXiv2015

Quantifying the non-ergodicity of scaled Brownian motion

We examine the non-ergodic properties of scaled Brownian motion, a non-stationary stochastic process with a time dependent diffusivity of the form $D(t)\simeq t^{α-1}$. We compute the ergodicity breaking parameter EB in the entire range of scaling exponents $α$, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths $T$ and short lag times $Δ$ the EB parameter as function of the scaling exponent $α$ has no divergence at $α=1/2$ and present the asymptotes for EB in different limits. We generalise the analytical and simulations results for the time averaged and ergodic properties of scaled Brownian motion in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion.

cond-mat.stat-mech↗

arXiv2015

Ultraslow scaled Brownian motion

We define and study in detail \emph{utraslow scaled Brownian motion (USBM)\/} characterised by a time dependent diffusion coefficient of the form $D(t)\simeq 1/t$. For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In an harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.

cond-mat.stat-mech↗