arXiv subjects

J. Łuczka

Publications and source records attributed to J. Łuczka.

At least 19 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

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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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

Periodic potential can enormously boost free particle transport induced by active fluctuations

Active fluctuations are detected in a growing number of systems due to self-propulsion mechanisms or collisions with active environment. They drive the system far from equilibrium and can induce phenomena which at equilibrium states are forbidden by e.g. fluctuation-dissipation relations and detailed balance symmetry. Understanding of their role in living matter is emerging as a challenge for physics. Here we demonstrate a paradoxical effect in which a free particle transport induced by active fluctuations can be boosted by many orders of magnitude when the particle is additionally subjected to a periodic potential. In contrast, within the realm of only thermal fluctuations the velocity of a free particle exposed to a bias is reduced when the periodic potential is switched on. The presented mechanism is significant for understanding nonequilibrium environments such as living cells where it can explain from a fundamental point of view why spatially periodic structures known as microtubules are necessary to generate impressively effective intracellular transport. Our findings can be readily corroborated experimentally e.g. in a setup comprising a colloidal particle in an optically generated periodic potential.

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arXiv2024

Intriguing properties of transport at the microscales: Langevin equation approach

We present a perspective of simple models of nonequilibrium directed transport described in terms of a Langevin equation formalism. We consider a Brownian particle under various circumstances and driven by thermal (equilibrium) and non-thermal (active) fluctuations. Three examples of startling behavior are unveiled: giant transport, multiple current reversal and negative mobility.

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arXiv2024

Effective mass approach to memory in non-Markovian systems

Recent pioneering experiments on non-Markovian dynamics done e.g. for active matter have demonstrated that our theoretical understanding of this challenging yet hot topic is rather incomplete and there is a wealth of phenomena still awaiting discovery. It is related to the fact that typically for simplification the Markovian approximation is employed and as a consequence the memory is neglected. Therefore methods allowing to study memory effects are extremely valuable. We demonstrate that a non-Markovian system described by the Generalized Langevin Equation (GLE) for a Brownian particle of mass $M$ can be approximated by the memoryless Langevin equation in which the memory effects are correctly reproduced solely via the effective mass $M^*$ of the Brownian particle which is determined only by the form of the memory kernel. Our work lays the foundation for an impactful approach which allows to readily study memory-related corrections to Markovian dynamics.

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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

Arcsine Law and Multistable Brownian Dynamics in a Tilted Periodic Potential

Multistability is one of the most important phenomena in dynamical systems, e.g. bistability enables the implementation of logic gates and therefore computation. Recently multistability has attracted a greatly renewed interest related to memristors and graphene structures, to name only a few. We investigate tristability in velocity dynamics of a Brownian particle subjected to a tilted periodic potential. It is demonstrated that the origin of this effect is attributed to the arcsine law for the velocity dynamics at the zero temperature limit. We analyze the impact of thermal fluctuations and construct the phase diagram for the stability of the velocity dynamics. It suggests an efficient strategy to control the multistability by changing solely the force acting on the particle or temperature of the system. Our findings for the paradigmatic model of nonequilibrium statistical physics apply to, inter alia, Brownian motors, Josephson junctions, cold atoms dwelling in optical lattices and colloidal systems.

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arXiv2021

Energy of a free Brownian particle coupled to thermal vacuum

Experimentalists have come to temperatures very close to absolute zero at which physics that was once ordinary becomes extraordinary. In such a regime quantum effects and fluctuations start to play a dominant role. In this context we study the simplest open quantum system, namely, a free quantum Brownian particle coupled to thermal vacuum, i.e. thermostat in the limiting case of absolute zero temperature. We analyze the average energy $E=E(c)$ of the particle from a weak to strong interaction strength $c$ between the particle and thermal vacuum. The impact of various dissipation mechanisms is considered. In the weak coupling regime the energy tends to zero as $E(c) \sim c\, \ln{(1/c)}$ while in the strong coupling regime it diverges to infinity as $E(c) \sim \sqrt{c}$. We demonstrate it for selected examples of the dissipation mechanisms defined by the memory kernel $γ(t)$ of the Generalized Langevin Equation. We reveal how at a fixed value of $c$ the energy $E(c)$ depends on the dissipation model: one has to compare values of the derivative $γ'(t)$ of the dissipation function $γ(t)$ at time $t=0$ or at the memory time $t=τ_c$ which characterizes the degree of non-Markovianity of the Brownian particle dynamics. The impact of low temperature is also presented.

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arXiv2020

Colossal Brownian yet non-Gaussian diffusion induced by nonequilibrium noise

We report on novel Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, the probability density for the particle spreading is Gaussian-like, however, the probability density for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area, this behaviour is not a consequence of either a space or time-dependent diffusivity, but is induced by external non-thermal noise acting on the particle dwelling in a periodic potential. The existence of the exponential tail in the increment statistics leads to colossal enhancement of diffusion, surpassing drastically the previously researched situation known under the label of "giant" diffusion. This colossal diffusion enhancement crucially impacts a broad spectrum of the first arrival problems, such as diffusion limited reactions governing transport in living cells.

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arXiv2020

Many faces of nonequilibrium: anomalous transport phenomena in driven periodic systems

We consider a generic system operating under non-equilibrium conditions. Explicitly, we consider an inertial classical Brownian particle dwelling a periodic structure with a spatially broken reflection symmetry. The particle is coupled to a bath at the temperature $T$ and is driven by an unbiased time-periodic force. In the asymptotic long time regime the particle operates as a Brownian motor exhibiting finite directed transport although no net biasing force acts on the system. Here we review and interpret in further detail recent own research on the peculiar transport behaviour for this setup. The main focus is put on those different emerging Brownian diffusion anomalies. Particularly, within the transient, time-dependent domain the particle is able to exhibit anomalous diffusive motion which eventually crosses over into normal diffusion only in the asymptotic long-time limit. In the latter limit this normal diffusion coefficient may even show a non-monotonic temperature dependence, meaning that it is not monotonically increasing with increasing temperature, but may exhibit instead an extended, intermediate minimum before growing again with increasing temperature.

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arXiv2019

Coexistence of absolute negative mobility and anomalous diffusion

Using extensive numerical studies we demonstrate that absolute negative mobility of a Brownian particle (i.e. the net motion into the direction opposite to a constant biasing force acting around zero bias) does coexist with anomalous diffusion. The latter is characterized in terms of a nonlinear scaling with time of the mean-square deviation of the particle position. Such anomalous diffusion covers "coherent" motion (i.e. the position dynamics x(t) approaches in evolving time a constant dispersion), ballistic diffusion, subdiffusion, superdiffusion and hyperdiffusion. In providing evidence for this coexistence we consider a paradigmatic model of an inertial Brownian particle moving in a one-dimensional symmetric periodic potential being driven by both an unbiased time-periodic force and a constant bias. This very setup allows for various sorts of different physical realizations.

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arXiv2019

Partition of energy for a dissipative quantum oscillator

We reveal a new face of the old clichéd system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems.Both mean kinetic energy $E_k$ and mean potential energy $E_p$ of the oscillator are expressed as $E_k = \langle \mathcal E_k \rangle$ and $E_p = \langle \mathcal E_p \rangle$, where $\langle \mathcal E_k \rangle$ and $ \langle \mathcal E_p \rangle$ are mean kinetic and potential energies per one degree of freedom of the thermostat which consists of harmonic oscillators too. The symbol $\langle ...\rangle$ denotes two-fold averaging: (i) over the Gibbs canonical state for the thermostat and (ii) over thermostat oscillators frequencies $ω$ which contribute to $E_k$ and $E_p$ according to the probability distribution $\mathbb{P}_k(ω)$ and $\mathbb{P}_p(ω)$, respectively. The role of the system-thermostat coupling strength and the memory time is analysed for the exponentially decaying memory function (Drude dissipation mechanism) and the algebraically decaying damping kernel.

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arXiv2019

On superstatistics of energy for a free quantum Brownian particle

We consider energetics of a free quantum Brownian particle coupled to thermostat of temperature $T$ and study this problem in terms of the lately formulated quantum analogue of the energy equipartition theorem. We show how this quantum counterpart can be derived from the Callen-Welton fluctuation-dissipation relation and rephrased in terms of superstatistics. We analyse the influence of the system-thermostat coupling strength and the memory time of the dissipation kernel on statistical characteristics of the particle energy and its specific heat.

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arXiv2019

Quantum partition of energy for a free Brownian particle: Impact of dissipation

We study the quantum counterpart of the theorem on energy equipartition for classical systems. We consider a free quantum Brownian particle modelled in terms of the Caldeira-Leggett framework: a system plus thermostat consisting of an infinite number of harmonic oscillators. By virtue of the theorem on the averaged kinetic energy $E_k$ of the quantum particle, it is expressed as $E_k = \langle \mathcal E_k \rangle$, where $\mathcal E_k$ is thermal kinetic energy of the thermostat per one degree of freedom and $\langle ...\rangle$ denotes averaging over frequencies $ω$ of thermostat oscillators which contribute to $E_k$ according to the probability distribution $\mathbb P(ω)$. We explore the impact of various dissipation mechanisms, via the Drude, Gaussian, algebraic and Debye spectral density functions, on the characteristic features of $\mathbb{P}(ω)$. The role of the system-thermostat coupling strength and the memory time on the most probable thermostat oscillator frequency as well as the kinetic energy $E_k$ of the Brownian particle is analysed.

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arXiv2016

Comment on 'Absolute negative mobility in a one-dimensional overdamped system'

Recently Ru-Yin Chen et al. (Phys. Lett. A 379 (2015) 2169-2173) presented results on the absolute negative mobility (ANM) in a one-dimensional overdamped system and claimed that a new minimal model of ANM was proposed. We suggest that the authors introduced a mistake in their calculations. Then we perform a precise numerical simulation of the corresponding Langevin equation to show that the ANM phenomenon does not occur in the considered system.

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arXiv2015

Efficiency of the SQUID Ratchet Driven by External Current

We study theoretically the efficiency of an asymmetric superconducting quantum interference device (SQUID) which is constructed as a loop with three capacitively and resistively shunted Josephson junctions. Two junctions are placed in series in one arm and the remaining one is located in the other arm. The SQUID is threaded by an external magnetic flux and driven by an external current of both constant (dc) and time periodic (ac) components. This system acts as a nonequilibrium ratchet for the dc voltage across the SQUID with the external current as a source of energy. We analyze the power delivered by the external current and find that it strongly depends on thermal noise and the external magnetic flux. We explore a space of the system parameters to reveal a set for which the SQUID efficiency is globally maximal. We detect the intriguing feature of the thermal noise enhanced efficiency and show how the efficiency of the device can be tuned by tailoring the external magnetic flux.

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