A collisional model of odd fluids: from Boltzmann equation to chiral hydrodynamics

TL;DR

This paper develops a microscopic collisional model of odd fluids using Boltzmann kinetic theory, demonstrating the emergence of odd responses like viscosity from particle collisions and predicting sign changes in response coefficients.

Contribution

It introduces a classical microscopic collisional model for odd fluids, linking Boltzmann theory to chiral hydrodynamics and computing response coefficients numerically.

Findings

Model exhibits many odd response terms.

Certain odd response coefficients can change sign with fixed external torque.

Method applicable to various collisional models.

Abstract

When the time-reversal and parity symmetries in a fluid are broken, transverse transport coefficients can arise in response to perturbations, an example being odd viscosity. We refer to these systems as odd fluids. While much progress has been made in the continuum theory of odd-viscous fluids, and non-collisional models for odd viscous fluids have been proposed, a classical microscopic description in which the transverse responses originate from collisions is lacking. In this paper, we show that a dilute granular gas of rough and inelastic particles driven by a constant torque is a minimal microscopic model of an odd fluid. By applying the methods of Boltzmann kinetic theory, we obtain a hydrodynamic description of the microscopic model. Then, using the method of adiabatic elimination, we numerically compute all the response coefficients of the model, explicitly showing that the model has many odd response terms. Our theory predicts that certain odd response coefficients can change sign even when the direction of the external torque is fixed. While we choose a particular case, the procedure we present can be applied to any collisional model. We also present a semi-quantitative method to determine the hydrodynamic variables of the theory by observing the eigenvalue spectrum of the linear collision operator.