arXiv subjects

Jerzy Łuczka

Publications and source records attributed to Jerzy Łuczka.

At least 19 recordsLinked to original sources

arXiv2024

Memory corrections to Markovian Langevin dynamics

Analysis of non-Markovian systems and memory induced phenomena poses an everlasting challenge for physics. As a paradigmatic example we consider a classical Brownian particle of mass $M$ subjected to an external force and exposed to correlated thermal fluctuations. We show that the recently developed approach to this system, in which its non-Markovian dynamics given by the Generalized Langevin Equation is approximated by its memoryless counterpart but with the effective particle mass $M^* < M$, can be derived within the Markovian embedding technique. Using this method we calculate the first and the second order memory correction to Markovian dynamics of the Brownian particle for the memory kernel represented as the Prony series. The second one lowers the effective mass of the system further and improves precision of the approximation. Our work opens the door for the derivation of higher order memory corrections to Markovian Langevin dynamics.

cond-mat.stat-mech↗

arXiv2023

Control of particle transport driven by active noise: strategy of amplification via a periodic potential

We extend our previous studies on a counter-intuitive effect in which a directed transport of a free Brownian particle induced by active fluctuations can be significantly enhanced when the particle is placed in a periodic potential. It is in clear contrast to a common situation when the velocity of the Brownian particle is notably reduced if the periodic potential is switched on. As a model of active fluctuations we employ white Poissonian shot noise. We reconsider the case of the skew-normal amplitude distribution of shot noise and focus on the impact of statistical characteristics of its amplitude like mean, variance and skewness on the magnitude of free particle transport enhancement. in particular, we detect intriguing oscillations of the rescaled velocity of the particle as a function of the variance. Our findings can be corroborated experimentally in both biological and artificial microscopic systems.

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arXiv2022

Diffusion coefficient of a Brownian particle in equilibrium and nonequilibrium: Einstein model and beyond

Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow down our survey for the case of the diffusion coefficient for a Brownian particle which can be modeled in the framework of Langevin dynamics. Our main focus will center on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds we consider a number of physical situations away from free Brownian motion and end with surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.

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arXiv2021

Velocity multistability vs ergodicity breaking in a biased periodic potential

Multistability, i.e. the coexistence of several attractors for a given set of system parameters is one of the most important phenomena occurring in dynamical systems. We consider it in velocity dynamics of a Brownian particle driven by thermal fluctuations and moving in a biased periodic potential. In doing so we focus on the impact of ergodicity - a concept which lies at the core of statistical mechanics. The latter implies that a single trajectory of the system is representative for the whole ensemble and as a consequence the initial conditions of the dynamics are fully forgotten. The ergodicity of the deterministic counterpart is strongly broken and we discuss how the velocity multistability depends on the starting position and velocity of the particle. While for non-zero temperature the ergodicity is in principle restored, in the low temperature regime the velocity dynamics is still affected by initial conditions due to weak ergodicity breaking. For moderate and high temperature the multistability is robust with respect to the choice of the starting position and velocity of the particle.

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arXiv2021

Conundrum of weak noise limit for diffusion in a tilted periodic potential

The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously hard to approach analytically or numerically. We reinvestigate in this context the paradigmatic model of nonequlibrium statistical physics consisting of inertial Brownian particle diffusing in a tilted periodic potential by exploiting the state of the art computer simulations of unprecedented time scale. In contrast to the previous results on this long standing problem we draw an inference that in the parameter regime for which the particle velocity is bistable the lifetime of ballistic diffusion diverges to infinity when thermal noise intensity tends to zero, i.e. an everlasting ballistic diffusion emerges. As a consequence the diffusion coefficient does not reach its stationary constant value.

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arXiv2021

Quantum Counterpart of Classical Equipartition of Energy

It is shown that the recently proposed quantum analogue of classical energy equipartition theorem for two paradigmatic, exactly solved models (i.e., a free Brownian particle and a dissipative harmonic oscillator) also holds true for all quantum systems which are composed of an arbitrary number of non-interacting or interacting particles, subjected to any confining potentials and coupled to thermostat with arbitrary coupling strength.

quant-ph↗

arXiv2021

Comment on "Deformed Fokker-Planck equation: inhomogeneous medium with a position-dependent mass"

In a recent paper by B. G. da Costa {\it et al.} [Phys. Rev. E 102, 062105(2020)], the phenomenological Langevin equation and the corresponding Fokker-Planck equation for an inhomogeneous medium with a position-dependent particle mass and position-dependent damping coefficient have been studied. The aim of this comment is to present a microscopic derivation of the Langevin equation for such a system. It is not equivalent to that in the commented paper.

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arXiv2019

Temperature induced tunable particle separation

An effective approach to isolation of sub-micro sized particles is desired to separate cancer and healthy cells or in therapy of Parkinson's and Alzheimer's disease. However, since bioparticles span a large size range comprising several orders of magnitude, development of an adequate separation method is a challenging task. We consider a collection of non-interacting Brownian particles of various sizes moving in a symmetric periodic potential and subjected to an external unbiased harmonic driving as well as a constant bias. We reveal a nonintuitive, yet efficient, separation mechanism based on thermal fluctuations induced negative mobility phenomenon in which particles of a given size move in a direction opposite to the applied bias. By changing solely temperature of the system one can separate particles of various strictly defined sizes. This novel approach may be important step towards development of point-of-care lab-on-a-chip devices.

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arXiv2019

Tunable mass separation via negative mobility

A prerequisite for isolating diseased cells requires a mechanism for effective mass-based separation. This objective, however, is generally rather challenging because typically no valid correlation exists between the size of the particles and their mass value. We consider an inertial Brownian particle moving in a symmetric periodic potential and subjected to an externally applied unbiased harmonic driving in combination with a constant applied bias. In doing so we identify a most efficient separation scheme which is based on the anomalous transport feature of negative mobility, meaning that the immersed particles move in the direction opposite to the acting bias. This work is first of its kind in demonstrating a tunable separation mechanism in which the particle mass targeted for isolation is effectively controlled over a regime of nearly two orders of mass-magnitude upon changing solely the frequency of the external harmonic driving. This approach may provide mass selectivity required in present and future separation of a diversity of nano and micro-sized particles of either biological or synthetic origin.

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arXiv2018

SQUID ratchet: Statistics of transitions in dynamical localization

We study occupation of certain regions of phase space of an asymmetric superconducting quantum interference device (SQUID) driven by thermal noise, subjected to an external ac current and threaded by a constant magnetic flux. Thermally activated transitions between the states which reflect three deterministic attractors are analyzed in the regime of the noise induced dynamical localization of the Josephson phase velocity, i.e. there is a temperature interval in which the conditional probability of the voltage to remain in one of the states is very close to one. Implications of this phenomenon on the dc voltage drop across the SQUID are discussed. We detect the emergence of the power law tails in a residence time probability distribution of the Josephson phase velocity and discuss the role of symmetry breaking in dynamical localization induced by thermal noise. This phenomenon illustrates how deterministic-like behaviour may be extracted from randomness by stochasticity itself.

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arXiv2018

Self--averaging of random quantum dynamics

Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating self-averaging with respect to its temporal unitary evolution. This phenomenon is quantified by the variance of the unitary matrix governing the time evolution of a finite dimensional quantum system which according to an asymptotic analysis decreases at least as $1/N$. For a special class of protocols (when the averaged Hamiltonian commutes at different times), we prove that for finite $N$ the distance (according to the Frobenius norm) between the averaged unitary evolution operator generated by the Hamiltonian $H$ and the unitary evolution operator generated by the averaged Hamiltonian $\langle H \rangle$ scales as $1/N$. Numerical simulations enlarge this result to a broader class of the non-commuting protocols.

quant-ph↗

arXiv2017

Subdiffusion via dynamical localization induced by thermal equilibrium fluctuations

We reveal the mechanism of subdiffusion which emerges in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven by both a time-periodic force and Gaussian white noise. In a tailored parameter set for which the deterministic counterpart is in a non-chaotic regime, subdiffusion is a long-living transient whose lifetime can be many, many orders of magnitude larger than characteristic time scales of the setup thus being amenable to experimental observations. As a reason for this subdiffusive behaviour in the coordinate space we identify thermal noise induced dynamical localization in the velocity (momentum) space. This novel idea is distinct from existing knowledge and has never been reported for any classical or quantum systems. It suggests reconsideration of generally accepted opinion that subdiffusion is due to road distributions or strong correlations which reflect disorder, trapping, viscoelasticity of the medium or geometrical constraints.

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arXiv2017

Energetics of a driven Brownian harmonic oscillator

We provide insights into energetics of a Brownian oscillator in contact with a heat bath and driven by an external unbiased time-periodic force that takes the system out of thermodynamic equilibrium. Solving the corresponding Langevin equation, we compute average kinetic and potential energies in the long-time stationary state. We also derive the energy balance equation and study the energy flow in the system. In particular, we identify the energy delivered by the external force, the energy dissipated by a thermal bath and the energy provided by thermal equilibrium fluctuations. Next, we illustrate Jarzynski work-fluctuation relation and consider the stationary state fluctuation theorem for the total work done on the system by the external force. Finally, by determining time scales in the system, we analyze the strong damping regime and discuss the problem of overdamped dynamics when inertial effects can be neglected.

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arXiv2017

Negative mobility of a Brownian particle: strong damping regime

We study impact of inertia on directed transport of a Brownian particle under non-equilibrium conditions: the particle moves in a one-dimensional periodic and symmetric potential, is driven by both an unbiased time-periodic force and a constant force, and is coupled to a thermostat of temperature T. Within selected parameter regimes this system exhibits negative mobility, which means that the particle moves in the direction opposite to the direction of the constant force. It is known that in such a setup the inertial term is essential for the emergence of negative mobility and it cannot be detected in the limiting case of overdamped dynamics. We analyse inertial effects and show that negative mobility can be observed even in the strong damping regime. We determine the optimal dimensionless mass for the presence of negative mobility and reveal three mechanisms standing behind this anomaly: deterministic chaotic, thermal noise induced and deterministic non-chaotic. The last origin has never been reported. It may provide guidance to the possibility of observation of negative mobility for strongly damped dynamics which is of fundamental importance from the point of view of biological systems, all of which in situ operate in fluctuating environments.

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arXiv2017

Work distributions for random sudden quantum quenches

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of hermitean matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature.

quant-ph↗

arXiv2017

Brownian ratchets: How stronger thermal noise can reduce diffusion

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e. a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force which takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by thermal noise and we explain this effect in terms of transition rates of a three-state stochastic model.

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arXiv2016

Non-monotonic temperature dependence of chaos-assisted diffusion in driven periodic systems

The spreading of a cloud of independent Brownian particles typically proceeds more effectively at higher temperatures, as it derives from the commonly known Sutherland-Einstein relation for systems in thermal equilibrium. Here, we report on a non-equilibrium situation in which the diffusion of a periodically driven Brownian particle moving in a periodic potential decreases with increasing temperature within a finite temperature window. We identify as the cause for this non-intuitive behaviour a dominant deterministic mechanism consisting of a few unstable periodic orbits embedded into a chaotic attractor together with thermal noise-induced dynamical changes upon varying temperature. The presented analysis is based on extensive numerical simulations of the corresponding Langevin equation describing the studied setup as well as on a simplified stochastic model formulated in terms of a three-state Markovian process. Because chaos exists in many natural as well as in artificial systems representing abundant areas of contemporary knowledge, the described mechanism may potentially be discovered in plentiful different contexts.

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arXiv2016

Diffusion anomalies in ac driven Brownian ratchets

We study diffusion in ratchet systems. As a particular experimental realization we consider an asymmetric SQUID subjected to an external ac current and a constant magnetic flux. We analyze mean-square displacement of the Josephson phase and find that within selected parameter regimes it evolves in three distinct stages: initially as superdiffusion, next as subdiffusion and finally as normal diffusion in the asymptotic long-time limit. We show how crossover times that separates these stages can be controlled by temperature and an external magnetic flux. The first two stages can last many orders longer than characteristic time scales of the system thus being comfortably detectable experimentally. The origin of abnormal behavior is noticeable related to the ratchet form of the potential revealing an entirely new mechanism of emergence of anomalous diffusion. Moreover, a normal diffusion coefficient exhibits non-monotonic dependence on temperature leading to an intriguing phenomenon of thermal noise suppressed diffusion. The proposed setup for experimental verification of our findings provides a new and promising testing ground for investigating anomalies in diffusion phenomena.

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