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 one to readily study memory-related corrections to Markovian dynamics.

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. Marchenko et al., Chaos 32, 113106 (2022)1054-150010.1063/5.0117902]. 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.

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., fluctuation-dissipation relations and detailed balance symmetry. Understanding 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.

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. 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.

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. We reinvestigate in this context the paradigmatic model of nonequilibrium statistical physics consisting of inertial Brownian particles diffusing in a tilted periodic potential by exploiting state-of-the-art computer simulations of an extremely long timescale. In contrast to previous results on this longstanding 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 the 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.

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.

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

In a recent paper by B. G. da Costa et al. [Phys. Rev. E 102, 062105 (2020)2470-004510.1103/PhysRevE.102.062105], 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.

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 [Formula: see text] 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 [Formula: see text] while in the strong coupling regime it diverges to infinity as [Formula: see text]. We demonstrate it for selected examples of the dissipation mechanisms defined by the memory kernel [Formula: see text] 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 [Formula: see text] of the dissipation function [Formula: see text] at time [Formula: see text] or at the memory time [Formula: see text] which characterizes the degree of non-Markovianity of the Brownian particle dynamics. The impact of low temperature is also presented.

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. This colossal diffusion enhancement crucially impacts a broad spectrum of the first arrival problems, such as diffusion limited reactions governing transport in living cells.

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. We discuss the relation of the later effect with the phenomenon of giant diffusion.

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 the 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 2 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 microsized particles of either biological or synthetic origin.

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 Ek and mean potential energy Ep of the oscillator are expressed as Ek = 〈εk〉 and Ep = 〈εp〉, where 〈εk〉 and 〈εp〉 are mean kinetic and potential energies per one degree of freedom of the thermostat which consists of harmonic oscillators too. The symbol 〈...〉 denotes two-fold averaging: (i) over the Gibbs canonical state for the thermostat and (ii) over thermostat oscillators frequencies ω which contribute to Ek and Ep according to the probability distribution [Formula: see text] and [Formula: see text], 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.

Energetics of an rf SQUID Coupled to Two Thermal Reservoirs.

We study energetics of a Josephson tunnel junction connecting a superconducting loop pierced by an external magnetic flux (an rf SQUID) and coupled to two independent thermal reservoirs of different temperature. In the framework of the theory of quantum dissipative systems, we analyze energy currents in stationary states. The stationary energy flow can be periodically modulated by the external magnetic flux exemplifying the rf SQUID as a quantum heat interferometer. We also consider the transient regime and identify three distinct regimes: monotonic decay, damped oscillations and pulse-type behavior of energy currents. The first two regimes can be controlled by the external magnetic flux while the last regime is robust against its variation.

Brownian motors in the microscale domain: enhancement of efficiency by noise.

We study a noisy drive mechanism for efficiency enhancement of Brownian motors operating on the microscale domain. It was proven [J. Spiechowicz et al., J. Stat. Mech. (2013) P02044] that biased noise η(t) can induce normal and anomalous transport processes similar to those generated by a static force F acting on inertial Brownian particles in a reflection-symmetric periodic structure in the presence of symmetric unbiased time-periodic driving. Here, we show that within selected parameter regimes, noise η(t) of the mean value 〈η(t)〉=F can be significantly more effective than the deterministic force F: the motor can move much faster, its velocity fluctuations are much smaller, and the motor efficiency increases several times. These features hold true in both normal and absolute negative mobility regimes. We demonstrate this with detailed simulations by resource to generalized white Poissonian noise. Our theoretical results can be tested and corroborated experimentally by use of a setup that consists of a resistively and capacitively shunted Josephson junction. The suggested strategy to replace F by η(t) may provide a new operating principle in which micro- and nanomotors could be powered by biased noise.

Squeezing of magnetic flux in nanorings.

We study superconducting and non-superconducting nanorings and look for non-classical features of magnetic flux passing through nanorings. We show that the magnetic flux can exhibit purely quantum properties in some peculiar states with quadrature squeezing. We identify a subset of Gazeau-Klauder states in which the magnetic flux can be squeezed and, within tailored parameter regimes, quantum fluctuations of the magnetic flux can be maximally reduced.

Two coupled Josephson junctions: dc voltage controlled by biharmonic current.

We study transport properties of two Josephson junctions coupled by an external shunt resistance. One of the junctions (say, the first) is driven by an unbiased ac current consisting of two harmonics. The device can rectify the ac current yielding a dc voltage across the first junction. For some values of coupling strength, controlled by an external shunt resistance, a dc voltage across the second junction can be generated. By variation of system parameters such as the relative phase or frequency of two harmonics, one can conveniently manipulate both voltages with high efficiency, e.g. changing the dc voltages across the first and second junctions from positive to negative values and vice versa.

Indirect control of transport and interaction-induced negative mobility in an overdamped system of two coupled particles.

One-dimensional transport of an overdamped Brownian particle biased by an external constant force does not exhibit negative mobility. However, when the particle is coupled to another particle, negative mobility can arise. We present a minimal model and propose a scenario in which only one (say, the first) particle is dc biased by a constant force and ac driven by an unbiased harmonic signal. In this way we intend to achieve two aims at once: (i) negative mobility of the first particle, which is exclusively induced by coupling to the second particle and (ii) indirect control of the transport properties of the second particle by manipulating the first particle only. For instance, the sign and amplitude of the averaged stationary velocity of the second particle can be steered by the driving applied to the first particle. As an experimentally realizable system, we propose two coupled resistively shunted Josephson junctions.

Transport driven by biharmonic forces: impact of correlated thermal noise.

We study an inertial brownian particle moving in a symmetric periodic substrate, driven by a zero-mean biharmonic force and correlated thermal noise. The brownian motion is described in terms of a generalized Langevin equation with an exponentially correlated gaussian noise term, obeying the fluctuation-dissipation theorem. We analyze impact of nonzero correlation time of thermal noise on transport properties of the brownian particle. We identify regimes where the increase of the correlation time intensifies long-time transport of the brownian particle. The opposite effect is also found: longer correlation time reduces the stationary velocity of the particle. The correlation time induced multiple current reversal is detected. We reveal that thermal noise of nonzero correlation time can radically enhance long-time velocity of the brownian particle in regimes where in the white noise limit the velocity is extremely small. All transport properties can be tested in the setup consisting of a resistively and capacitively shunted Josephson junction device.

Current-flux characteristics in mesoscopic non-superconducting rings.

We propose four different mechanisms responsible for the paramagnetic or diamagnetic persistent currents in normal metal rings and determine the circumstances for changes of the current from paramagnetic to diamagnetic and vice versa. This might qualitatively reproduce the experimental results of Bluhm et al (2009 Phys. Rev. Lett. 102 136802).

Current in Hubbard rings manipulated via magnetic flux.

We study currents in a quantum ring threaded by a magnetic flux which is varied in an arbitrary way from an initial constant value φ(1) at time t(1) to a final constant value φ(2) at time t(2). We analyze how the induced currents for t > t(2) can be controlled by the rate of flux variation [Formula: see text]. The dynamics of electrons in the ring is described using the Hubbard and the extended Hubbard models. In the Hubbard model with infinite on-site repulsion the current for t > t(2) is shown to be independent of the flux variation before t(2) and is fully determined by a solution of the initial equilibrium problem and by the value φ(2) of the flux. For intermediate values of the interaction strength the current displays regular or irregular time oscillations and the amplitude of oscillations is sensitive to the rate of the flux changing [Formula: see text]: slow changes of the flux result in small amplitudes of the current oscillations and vice versa. We demonstrate that the time dependence of the induced current bears information on electronic correlations. Our results have important implications for not only mesoscopic rings but also the designing of quantum motors built out of ring-shaped optical lattices.