Dynamics of non-Markovian systems: Markovian embedding versus effective mass approach.

Dynamics of non-Markovian systems is a classic problem yet it attracts everlasting activity in physics and beyond. A powerful tool for modeling such setups is the generalized Langevin equation, however, its analysis typically poses a major challenge even for numerical means. For this reason, various approximations have been proposed over the years that simplify the original model.

Memory-induced absolute negative mobility.

Non-Markovian systems form a broad area of physics that remains greatly unexplored despite years of intensive investigations. The spotlight is on memory as a source of effects that are absent in their Markovian counterparts. In this work, we dive into this problem and analyze a driven Brownian particle moving in a spatially periodic potential and exposed to correlated thermal noise.

Memory Corrections to Markovian Langevin Dynamics.

Analysis of non-Markovian systems and memory-induced phenomena poses an everlasting challenge in the realm of physics. As a paradigmatic example, we consider a classical Brownian particle of mass 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∗ View Article and Find Full Text PDF

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.

Mechanism for giant enhancement of transport induced by active fluctuations.

Understanding the role of active fluctuations in physics is a problem in statu nascendi appearing both as a hot topic and a major challenge. The reason for this is the fact that they are inherently nonequilibrium. This feature opens a landscape of phenomena yet to be explored that are absent in the presence of thermal fluctuations alone.

Temperature anomalies of oscillating diffusion in ac-driven periodic systems.

We analyze 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 quasiperiodic oscillations as a function of the amplitude of the time-periodic force [I. G.

Paradoxical nature of negative mobility in the weak dissipation regime.

We reinvestigate a paradigmatic model of nonequilibrium statistical physics consisting of an inertial Brownian particle in a symmetric periodic potential subjected to both a time-periodic force and a static bias. In doing so, we focus on the negative mobility phenomenon in which the average velocity of the particle is opposite to the constant force acting on it. Surprisingly, we find that in the weak dissipation regime, thermal fluctuations induce negative mobility much more frequently than it happens if dissipation is stronger.

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 an active environment. They drive the system far from equilibrium and can induce phenomena that are forbidden at equilibrium states by, e.g.

Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond.

The diffusion of small particles is omnipresent in many 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 our survey to the case of the diffusion coefficient for a Brownian particle that can be modeled in the framework of Langevin dynamics.

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 that carry the leading contribution to the diffusion coefficient.

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.

Colossal Brownian yet non-Gaussian diffusion in a periodic potential: Impact of nonequilibrium noise amplitude statistics.

Last year, Białas et al. [Phys. Rev.

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 to phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously hard to approach analytically or numerically.

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.

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.

Colossal Brownian yet non-Gaussian diffusion induced by nonequilibrium noise.

We report on Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, and the probability density for the particle spreading is Gaussian like, but the probability density for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area, this behavior is not a consequence of either a space- or time-dependent diffusivity, but is induced by external nonthermal 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, drastically surpassing the previously researched situation known as "giant" diffusion.

Tunable particle separation via deterministic absolute negative mobility.

Particle isolation techniques are in the spotlight of many areas of science and engineering. In food industry, a harmful bacterial activity can be prevented with the help of separation schemes. In health care, isolation techniques are used to distinguish cancer and healthy cells or in therapy for Alzheimer's and Parkinson's diseases.

Diffusion in a biased washboard potential revisited.

The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize the diffusion of underdamped Brownian motion in a biased periodic potential and analyze regimes in which a diffusion coefficient decreases with increasing temperature within a finite temperature window. Comprehensive numerical simulations of the corresponding Langevin equation performed with unprecedented resolution allow us to construct a phase diagram for the occurrence of the nonmonotonic temperature dependence of the diffusion coefficient.

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.

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.

Sample Entropy of sEMG Signals at Different Stages of Rectal Cancer Treatment.

Information theory provides a spectrum of nonlinear methods capable of grasping an internal structure of a signal together with an insight into its complex nature. In this work, we discuss the usefulness of the selected entropy techniques for a description of the information carried by the surface electromyography signals during colorectal cancer treatment. The electrical activity of the external anal sphincter can serve as a potential source of knowledge of the actual state of the patient who underwent a common surgery for rectal cancer in the form of anterior or lower anterior resection.

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 and mean potential energy E of the oscillator are expressed as E = 〈ε〉 and E = 〈ε〉, where 〈ε〉 and 〈ε〉 are mean kinetic and potential energies per one degree of freedom of the thermostat which consists of harmonic oscillators too.

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.

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.

Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation.

We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry.