Absolute negative mobility in a vibrational motor

Absolute negative mobility of an inertial Brownian particle in an oscillating potential

Transport of an inertial Brownian particle in an oscillating potential is numerically investigated in the presence of an external constant force. The oscillating potential can break thermodynamic equilibrium. Within appropriate parameter regimes, the particle moves in a direction opposite to the constant force, which means that the system can exhibit the phenomenon of absolute negative mobility (ANM). Furthermore, it may be inferred from the bifurcation diagrams that ANM originates from chaotic-periodic transitions, where the particle subjected to a constant force performs reverse periodic motion due to continuous reverse driving by the oscillating potential. Based on GPU acceleration techniques, we present the distribution of ANM in the parameter space and analyze how the ANM depends on the system parameters. These results are robust in a wide range of parameters and may pave the way to the experimental realization of ANM.

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. We show that the absolute negative mobility effect, in which the net movement of the particle is in the direction opposite to the average force acting on it, may be induced by the memory of the setup. To explain the origin of this phenomenon, we resort to the recently developed effective mass approach to dynamics of non-Markovian systems.

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. In particular, for the very first time, we report a parameter set in which thermal noise causes this effect in the nonlinear response regime. Moreover, we show that the coexistence of deterministic negative mobility and chaos is routinely encountered when approaching the overdamped limit in which chaos does not emerge rather than near the Hamiltonian regime of which chaos is one of the hallmarks. On the other hand, at non-zero temperature, the negative mobility in the weak dissipation regime is typically affected by weak ergodicity breaking. Our findings can be corroborated experimentally in a multitude of physical realizations, including, e.g., Josephson junctions and cold atoms dwelling in optical lattices.

Anomalous transport of a classical wave-particle entity in a tilted potential

A classical wave-particle entity in the form of a millimetric walking droplet can emerge on the free surface of a vertically vibrating liquid bath. Such wave-particle entities have been shown to exhibit hydrodynamic analogs of quantum systems. Using an idealized theoretical model of this wave-particle entity in a tilted potential, we explore its transport behavior. The integro-differential equation of motion governing the dynamics of the wave-particle entity transforms to a Lorenz-like system of ordinary differential equations that drives the particle's velocity. Several anomalous transport regimes such as absolute negative mobility, differential negative mobility, and lock-in regions corresponding to force-independent mobility are observed. These observations motivate experiments in the hydrodynamic walking-droplet system for the experimental realizations of anomalous transport phenomena.

Entropic vibrational resonance

We demonstrate the existence of vibrational resonance associated with the presence of an uneven boundary. When the motion of a Brownian particle is confined in a region with an uneven boundary, constrained to a double cavity, a high-frequency signal may produce a peak in the spectral power amplification of the other low-frequency signal and therefore to the appearance of the vibrational resonance phenomenon. The mechanism of vibrational resonance in constrained boundaries is different from that in energetic potentials and is termed entropic vibrational resonance (EVR). The EVR can be observed even if the bias force is absent in any direction. Through careful analysis, we clarify two types of mechanisms of the EVR. The one mechanism is ascribed to the transition from a bistable system to a monostable system, and the other corresponds to the match between the escape rate and the natural frequency of the low-frequency signal. Our work merges the vibrational resonance with an uneven boundary, thus extending the scope of the vibrational resonance and shedding new light on the concept of resonance.

Negative friction and mobilities induced by friction fluctuation

We study the transport phenomena of an inertial Brownian particle in a symmetric potential with periodicity, which is driven by an external time-periodic force and an external constant bias for both cases of the deterministic dynamics and the existence of friction coefficient fluctuations. For the deterministic case, it is shown that for suitable parameters, the existence of certain appropriate friction coefficients can enhance the transport of the particle, which may be interpreted as the negative friction coefficient; additionally, there coexist absolute, differential negative, and giant positive mobilities with increasing friction coefficients in the system. We analyze physical mechanisms hinted behind these findings via basins of attraction. For the existence of friction coefficient fluctuations, it is shown that the fluctuation can enhance or weaken, even eliminate these phenomena. We present the probability distribution of the particle's velocity to interpret these mobilities and the suitable parameters' regimes of these phenomena. In order to further understand the physical mechanism, we also study diffusions corresponding to these mobilities and find that for the small fluctuation, the negative friction appears, and there coexists absolute negative mobility, superdiffusion, and ballistic diffusion, whereas all of them vanish for the large fluctuation. Our findings may extensively exist in materials, including different defects, strains, the number of interfacial hydrogen bonds, the arrangements of ions, or graphite concentrations, which hints at the existence of different friction coefficients.

Spontaneous rectification and absolute negative mobility of inertial Brownian particles induced by Gaussian potentials in steady laminar flows

We study the transport of inertial Brownian particles in steady laminar flows in the presence of two-dimensional Gaussian potentials. Through extensive numerical simulations, it is found that the transport is sensitively dependent on the external constant force and the Gaussian potential. Within tailored parameter regimes, the system exhibits a rich variety of transport behaviors. There exists the phenomenon of spontaneous rectification (SR), where the directed transport of particles can occur in the absence of any external driving forces. It is found that SR of the particles can be manipulated by the spatial position of the Gaussian potential. Moreover, when the potential lies at the center of the cellular flow, the system exhibits absolute negative mobility (ANM), i.e., the particles can move in a direction opposite to the constant force. More importantly, the phenomenon of ANM induced by Gaussian potentials is robust in a wide range of system parameters and can be further strengthened with the optimized parameters, which may pave the way to the implementation of related experiments.

Symmetry breaking: Abnormal transport induced by mass modulation

Here, we investigate transport of an inertial particle in a symmetric periodic potential and subjected to an external signal, such that mass of the particle is modulated sinusoidally. Our numerical results indicate that the mass modulation can induce abnormal transport in the system, whereas no current appears in the case of constant mass. In the absence of external bias, direction of mean velocity of the particle changes several times as amplitude and frequency of the mass modulation are varied, i.e., a multiple current reversals (CR) phenomenon. The multiple CRs result from temporal symmetry breaking of the system. In the presence of external bias, multiple absolute negative mobilities (ANM) take place in the system. Intrinsic physical mechanisms responsible for the occurrence of the multiple ANMs are analyzed in detail.

Vibrational resonance in an inhomogeneous medium with periodic dissipation

The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.

Multiple absolute negative mobilities

In this paper, we investigate transport of an inertial particle in a spatially symmetric potential and subjected to two harmonic signals with different frequencies in both deterministic and stochastic cases. Numerical results indicate that: (i) In the deterministic case, the two harmonic signals can induce many (up to six) segments of negative slopes in the curve of mean velocity vs. external constant force, i.e., a multiple absolute negative mobilities (ANMs) effect. But the occurrence of the effect depends on their frequencies and amplitudes. (ii) For the stochastic case, the multiple ANMs relay on stable index and symmetry parameter of the Lévy noise. In the case of symmetric noise, appropriate stable index makes the multiple ANMs be the strongest. Our further investigations indicate that an indispensable condition for the multiple ANMs to occur in the system is the temporal symmetry breaking by one multiplicative periodic signal and one additive periodic signal.

Deterministic particle transport in a ratchet flow

This study is motivated by the issue of the pumping of particle through a periodic modulated channel. We focus on a simplified deterministic model of small inertia particles within the Stokes flow framework that we call "ratchet flow." A path-following method is employed in the parameter space in order to retrace the scenario which from bounded periodic solutions leads to particle transport. Depending on whether the magnitude of the particle drag is moderate or large, two main transport mechanisms are identified in which the role of the parity symmetry of the flow differs. For large drag, transport is induced by flow asymmetry, while for moderate drag, since the full transport solution bifurcation structure already exists for symmetric settings, flow asymmetry only makes the transport effective. We analyzed the scenarios of current reversals for each mechanism as well as the role of synchronization. In particular we show that, for large drag, the particle drift is similar to phase slip in a synchronization problem.

Absolute negative mobility induced by potential phase modulation

We investigate the transport properties of a particle subjected to a deterministic inertial rocking system, under a constant bias, for which the phase of the symmetric spatial potential used is time modulated. We show that this modulated phase, assisted by a periodic driving force, can lead to the occurrence of the so-called absolute negative mobility (ANM), the phenomenon in which the particle surprisingly moves against the bias. Furthermore, we discover that ANM predominantly originates from chaotic-periodic transitions. While a detailed mechanism of ANM remains unclear, we show that one can manipulate the control parameters, i.e., the amplitude and the frequency of the phase, in order to enforce the motion of the particle in a given direction. Finally, for this experimentally realizable system, we devise a two-parameter current plot which may be a good guide for controlling ANM.

Persistence of uphill anomalous transport in inhomogeneous media

For systems out of equilibrium and subjected to a static bias force it can often be expected that particle transport will usually follow the direction of this bias. However, counterexamples exist where particles exhibit uphill motion (known as absolute negative mobility, ANM), particularly in the case of coupled particles. Examples in single particle deterministic systems are less common. Recently, in one such example, uphill motion was shown to occur for an inertial driven and damped particle in a spatially symmetric periodic potential. The source of this anomalous transport was a combination of two periodic driving signals which together are asymmetric under time reversal. In this paper we investigate the phenomena of ANM for a deterministic particle evolving in a periodic and symmetric potential subjected to an external unbiased periodic driving and nonuniform space-dependent damping. It will be shown that this system exhibits a complicated response behavior as certain control parameters are varied, most notably being enhanced parameter regimes exhibiting ANM as the static bias force is increased. Moreover, the solutions exhibiting ANM are shown to be, at least over intermediate time periods, superdiffusive, in contrast to the solutions that follow the bias where the diffusion is normal.