Kinetic Theory of Chiral Active Disks: Odd Transport and Torque Density

TL;DR

This paper develops a kinetic theory for chiral active disks, revealing how chirality induces odd transport phenomena like odd viscosity and torque density, with analytical predictions validated by simulations.

Contribution

It introduces a minimal kinetic model for chiral fluids that analytically predicts odd transport coefficients, bridging microscopic collisions and macroscopic odd transport behaviors.

Findings

Analytical expressions for odd viscosity, thermal conductivity, and diffusivity.

Good agreement between Chapman-Enskog predictions and numerical simulations.

Chirality induces a nonzero torque density and antisymmetric stress in the fluid.

Abstract

Parity-odd transport is a central signature of chiral fluids, yet analytical predictions are sparse. Here, we introduce a minimal two-dimensional hard-disk gas in which chirality arises solely from a collision-induced transverse impulse. Motivated by granular spinners, collisions are dissipative and inject orbital angular momentum through a fixed tangential ``kick'' at contact. Starting from a Boltzmann-Enskog description, we derive nonlinear hydrodynamic equations for density, momentum, and temperature, and show that chirality generates an antisymmetric homogeneous stress corresponding to a nonzero torque density. In the dilute limit, a Chapman-Enskog expansion yields analytical predictions for transport coefficients, including odd viscosity, odd thermal conductivity, and odd self-diffusivity, in good agreement with numerical simulations. This minimal kinetic model can serve as a foundation for systematic coarse-graining of chiral fluids and as a tractable benchmark for gaining insight into odd transport across a broader class of chiral systems.