Odd Active Solids: Vortices, Velocity Oscillations and Dissipation-Free Modes

TL;DR

This paper investigates how odd forces in active solids induce vortex structures, velocity oscillations, and dissipation-free modes, revealing new non-equilibrium behaviors in systems with non-potential interactions.

Contribution

It introduces a coarse-grained model of active solids with odd forces, demonstrating their role in generating vortex dynamics and oscillations, and explores stability and nonlinear effects.

Findings

Odd forces can counteract dissipation, leading to quasi-dissipation-free excitations.

Transverse instabilities occur when odd force strength exceeds a threshold.

Nonlinear interactions suppress short-wavelength velocity divergence, enabling exploration of unstable regimes.

Abstract

A wide range of physical and biological systems, including colloidal magnets, granular spinners, and starfish embryos, are characterized by strongly rotating units that give rise to odd viscosity and odd elasticity. These active systems can be described using a coarse-grained model in which the pairwise forces between particles include a transverse component compared to standard interactions due to a central potential. These non-potential, additional forces, referred to as odd interactions, do not conserve energy or angular momentum and induce rotational motion. Here, we study a two-dimensional crystal composed of inertial Brownian particles that interact via odd forces and are in thermal contact with their environment. In the underdamped regime, the energy injected by odd forces can counteract dissipation due to friction, leading to quasi-dissipation-free excitations with finite frequency and wavelength. In the resulting non-equilibrium steady state, the system exhibits angular momentum and velocity correlations. When the strength of the odd forces exceeds a certain threshold or friction is too low, a crystal with only harmonic springs becomes linearly unstable due to transverse fluctuations. This instability can be mitigated by introducing nonlinear central interactions, which suppress the divergence of short-wavelength velocity fluctuations and allows us to numerically explore the linearly unstable regime. This is characterized by pronounced temporal oscillations in the velocity featuring the existence of vortex structures and kinetic temperature values larger than the thermal temperature.