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

TL;DR

This paper reveals how asymmetric limit cycles in a Lorenz-inspired model of active particles lead to anomalous mobility behaviors, including giant negative and positive mobility, driven by the system's chaotic dynamics and memory effects.

Contribution

It introduces a minimal Lorenz-based model for active particles that explains the emergence of anomalous transport phenomena due to asymmetric limit cycles and chaos.

Findings

Coexistence of giant negative and positive mobility in the model

Asymmetric limit cycles induce anomalous transport behaviors

Memory effects influence the particle's response to bias force

Abstract

On applying a small bias force, non-equilibrium 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.