Chiral active gyrator: Memory induced direction reversal of rotational motion

TL;DR

The paper addresses how a chiral active particle behaves when confined in a 2D anisotropic harmonic potential and coupled to orthogonal heat baths in a viscoelastic medium with memory. It derives an exact expression for the steady-state angular momentum $⟨ω⟩$, decomposed into a gyration term proportional to $-ΔT α Γ$ and a chiral-memory term proportional to $Ω$ with memory scales $t_c$ and $t'_c$. A key finding is memory-induced reversal of rotation even at $ΔT=0$, contingent on nonzero $α$, with rotation tunable by $ΔT$, $α$, $Ω$, $t_c$, and $t'_c$; in the viscous limit, reversal occurs only along a neutral line where competing contributions cancel. The results reveal a novel non-Markovian mechanism for directional control in active matter, with potential implications for micro-swimmers in bio-fluids and memory-enabled rotors. Overall, the work provides a theoretical framework for exploiting viscoelastic memory to induce and control rotational states in active systems.

Abstract

We theoretically explore the dynamics of a chiral active Ornstein Uhlenbeck particle confined in a two-dimensional anisotropic harmonic trap. The particle is driven by chirality and is coupled to two orthogonal heat baths, potentially at two different temperatures. Using both analytical approach and numerical simulation, we explore the rotational dynamics of the particle in both viscous and viscoelastic environments. While the particle is suspended in a viscoelastic bath, characterized by a finite memory time scale, we interestingly observe that even in the absence of a temperature gradient, the angular momentum changes its sign as a function of the memory timescale, reflecting the direction reversal of rotational motion of the particle, and it is solely due to the interplay between memory and chirality. This direction reversal is a distinct memory-induced phenomenon and does not occur in the viscous limit. Moreover, increasing (or decreasing) the temperature gradient shifts the magnitude of the angular momentum further into the negative (or positive) direction, selecting a unique direction of rotation for the particle throughout the activity-memory parameter space. However, in the viscous limit, the direction reversal of the rotational motion is still possible but occurs only across a neutral line in parameter space, along which the contributions from both chirality and thermal anisotropy to the net angular momentum exactly cancel. These results highlight a distinct mechanism for directional control in active systems, with memory enabling reversal phenomena unique to viscoelastic media.

Figures (8)

• Figure 1: The 2D parametric plot of $\langle \omega \rangle$ [Eq. \ref{['eq:omega_gen']}] as a function of $t_c$ and $t_c'$ is shown in (a) for $\Delta T = 0$, (b) for $\Delta T = 1.5$, (c) for $\Delta T = 3$, (d) for $\Delta T = -0.1$, (e) for $\Delta T = -0.5$, and (f) for $\Delta T = -1$. The color map represents the value of $\langle \omega \rangle$. The common parameters are $\alpha = 0.8$, $m = \Omega = \xi_0 = \omega_0 = \Gamma = 1$.
• Figure 2: $\langle \omega \rangle$ [Eq. \ref{['eq:omega_gen_deltaT0']}] as a function of $t_c'$ is shown in (a) for $\Delta T = 0$, $\Omega = 1$ and different values of the $t_c$, and in (b) for $\Omega = 0$ and various values of $\Delta T$. The parameters used are $m = \Gamma = \omega_0 = \xi_0 = 1$ and $\alpha = 0.8$. The solid line represents the analytical results, and the dots represent the results obtained from numerical simulation.
• Figure 3: $\langle \omega \rangle$ [Eq. \ref{['eq:omega_viscous_a0']}] as a function of the $t_c$ for different values of $\Omega$ is shown in (a), and as a function of $\Omega$ for various fixed values of $t_c$ is shown in (b). The other common parameters used are $m = \Gamma = \xi_0 = \omega_0 = 1$. The solid line represents the analytical results, and the dots represent the results obtained from numerical simulation.
• Figure 4: $\langle \omega \rangle$ [Eq. \ref{['eq:omega_viscous']}] as a function of $t_c$ for different values of $\alpha$ is shown in (a) for $\Delta T = 1$, in (b) for $\Delta T = 2$, in (c) for $\Delta T = 3$ and in (d) for $\Delta T = 4$. The other common parameters are $\Omega = \omega_0 = \Gamma = m = \xi_0 = 1$. The solid line represents the analytical results, and the dots represent the results obtained from numerical simulation.
• Figure 5: $\langle \omega \rangle$ [Eq. \ref{['eq:omega_viscous']}] as a function of $\Omega$ for different values of $\Delta T$ in (a) for $\alpha = -0.5$ and in (b) for $\alpha = 0.5$. Other fixed parameters are $t_c = \omega_0 = \Gamma = m = \xi_0 = 1$. The solid line represents the analytical results, and the dots represent the results obtained from numerical simulation.