Absolute negative mobility of active polymer chains in steady laminar flows

Asymmetric limit cycles within Lorenz chaos induce anomalous mobility for a memory-driven active particle

On applying a small bias force, nonequilibrium systems may respond in paradoxical ways such as with giant negative mobility (GNM)-a large net drift opposite to the applied bias, or giant positive mobility (GPM)-an anomalously large drift in the same direction as the applied bias. Such behaviors have been extensively studied in idealized models of externally driven passive inertial particles. Here, we consider a minimal model of a memory-driven active particle inspired from experiments with walking and superwalking droplets, whose equation of motion maps to the celebrated Lorenz system. By adding a small bias force to this Lorenz model for the active particle, we uncover a dynamical mechanism for simultaneous emergence of GNM and GPM in the parameter space. Within the chaotic sea of the parameter space, a symmetric pair of coexisting asymmetric limit cycles separate and migrate under applied bias force, resulting in anomalous transport behaviors that are sensitive to the active particle's memory. Our work highlights a general dynamical mechanism for the emergence of anomalous transport behaviors for active particles described by low-dimensional nonlinear models.

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.