arXiv subjects

I. G. Marchenko

Publications and source records attributed to I. G. Marchenko.

8 recordsLinked to original sources

arXiv2026

Can the Brownian diffusion coefficient be reconstructed from Lyapunov exponents?

We consider an ac-driven particle moving in a spatially periodic and symmetric potential. In the zero- temperature limit, for the analyzed parameter set, its dynamics is non-chaotic and the particle does not manifest diffusive properties. At non-zero temperatures, the asymptotic long-time motion follows normal (Brownian) diffusion. Recent studies have shown that within tailored parameter regimes, the diffusion coef- ficient is a quasiperiodic function of the external driving amplitude [1]. Although no general relation between Lyapunov exponents and Brownian diffusion exists, we demonstrate that the quasiperiodic diffusion coefficient at non-zero temperature can be accurately reconstructed from the maximal Lyapunov exponent of the corresponding deterministic system (at vanishing temperature). We propose an approximate formula for this purpose, which shows good agreement with numerical simulations, although some discrepancies are detected in the vicinity of the local maxima of the diffusion coefficient. Finally, we examine the robustness of the correlation between diffusion and the Lyapunov exponent under variations of the system parameters.

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arXiv2025

Approach to nonequilibrium: from anomalous to Brownian diffusion via non-Gaussianity

Recent progress in experimental techniques such as single particle tracking allows to analyze both nonequilibrium properties and approach to equilibrium. There are examples showing that processes occurring at finite timescales are distinctly different than their equilibrium counterparts. In this work we analyze a similar problem of approach to nonequilibrium. We consider an archetypal model of nonequilibrium system consisting of a Brownian particle dwelling in a spatially periodic potential and driven by an external time-periodic force. We focus on a diffusion process and monitor its development in time. In the presented parameter regime the excess kurtosis measuring the Gaussianity of the particle displacement distribution evolves in a non-monotonic way: first it is negative (platykurtic form), next it becomes positive (leptokurtic form) and then decays to zero (mesokurtic form). Despite the latter fact diffusion in the long time limit is Brownian, yet non-Gaussian. Moreover, we discover a correlation between non-Gaussianity of the particle displacement distribution and transient anomalous diffusion behavior emerging for finite timescales.

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arXiv2024

Giant increase of diffusion by small rise of friction

Diffusion coefficient usually decreases when friction increases. We analyze the opposite behavior in the paradigmatic system consisting of an inertial Brownian particle moving in a symmetric spatially periodic potential and driven by an unbiased time periodic force. For tailored parameter set in strong dissipation regime the particle spreading can be giantly amplified: if the friction is twice as large then the diffusion grows up to five orders of magnitude. The mechanism lying behind this effect is related to bifurcation of periodic orbits oscillating around the potential maximum and their symmetric displacement towards the adjacent potential minima when the friction coefficient increases. On the other hand, in the weak dissipation regime, where the increase of diffusion vs friction is also observed, the effect is induced by a non-monotonic change of population of the running orbits. However, in this regime the enhancement of diffusion is much smaller.

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arXiv2023

Temperature anomalies of oscillating diffusion in ac-driven periodic systems

We analyse the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low friction regime in which the diffusion coefficient shows giant damped quasi-periodic oscillations as a function of the amplitude of the time-periodic force [I. G. Marchenko et al., Chaos 32, 113106 (2022)]. We find out that when temperature grows the diffusion coefficient increases at its minima, however, it decreases at the maxima within a finite temperature window. This curious behavior is explained in terms of the deterministic dynamics perturbed by thermal fluctuations and mean residence time of the particle in the locked and running trajectories. We demonstrate that temperature dependence of the diffusion coefficient can be accurately reconstructed from the stationary probability to occupy the running trajectories.

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arXiv2022

Giant oscillations of diffusion in ac-driven periodic systems

We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is normal in the long time limit and exhibits intriguing giant damped quasiperiodic oscillations as a function of the external driving amplitude. As the mechanism behind this effect we identify the corresponding oscillations of difference in the number of locked and running trajectories which carries the leading contribution to the diffusion coefficient. Our findings can be verified experimentally in a multitude of physical systems including colloidal particles, Josephson junction or cold atoms dwelling in optical lattices, to name only a few.

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arXiv2021

On dispersionless transport in washboard potentials

We reassess the "dispersionless transport regime" of Brownian particles in tilted periodic potentials. We show that the particles exhibit normal diffusive motion right after transitioning into the running state dragged by the constant bias force. No special transient dynamics appears, contrary to conjectures in the previous studies. The observed flat segment in the dispersion evolution curve is solely due to the broad spatial distribution of particles formed in the early superdiffusion stage. We quantitatively describe the whole evolution of the distribution function during superdiffusion and the transition to the normal diffusion that follows, in the framework of the 2-well potential in the velocity space model. We show that the superdiffusion exponent is $α=3$. Estimate of the duration of the ostensible "dispersionless regime" is provided. It is shown to diverge exponentially as the temperature decreases to zero.

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arXiv2013

A simple phenomenologic model for particle transport in space-periodic potentials in underdamped systems

We consider the motion of an underdamped Brownian particle in a tilted periodic potential in a wide temperature range. Based on the previous data [1] and the new simulation results we show that the underdamped motion of particles in space-periodic potentials can be considered as the overdamped motion in the velocity space in the effective double-well potential. Simple analytic expressions for the particle mobility and diffusion coefficient have been derived with the use of the presented model. The results of analytical computations match well with numerical simulation data.

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arXiv2011

Abnormal Temperature-Diffusion Relationship in the External Periodic Fields

Using the methods of computer modeling this scientific paper studies the special features of diffusion of the particles subjected to the external periodic force in the crystal lattice. The particle motion is described by a Langevin equation. The systems with a low friction coefficient may experience abnormal diffusion modes, in particular hyperdiffusion and subdiffusion. The applied external time-periodic field causes limitation of time intervals of abnormal diffusion making the diffusion coefficients dependent on frequency of applied force. The temperature relationships of these values have been calculated. It has been shown that the diffusion coefficients behave in abnormal ways as the temperature changes. In some temperature intervals the diffusion may increase as the temperature drops. Location and width of these intervals depend on the frequency of the external field.

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