Anisotropic odd viscosity via time-modulated drive

TL;DR

This paper demonstrates how time-modulated driving forces can induce anisotropic, dissipationless odd viscosity in out-of-equilibrium fluids, leading to novel flow behaviors and mechanical responses.

Contribution

It introduces a method to engineer anisotropic odd viscosity in classical fluids through time-dependent drives, expanding understanding beyond quantum Hall systems.

Findings

Anisotropic odd viscosity can be generated in driven fluids.

Time-modulated drives induce tensorial, dissipationless viscosity components.

Anisotropic odd viscosity influences bulk flow and shape distortions.

Abstract

At equilibrium, the structure and response of ordered phases are typically determined by the spontaneous breaking of spatial symmetries. Out of equilibrium, spatial order itself can become a dynamically emergent concept. In this article, we show that spatially anisotropic viscous coefficients and stresses can be designed in a far-from-equilibrium fluid by applying to its constituents a time-modulated drive. If the drive induces a rotation whose rate is slowed down when the constituents point along specific directions, anisotropic structures and mechanical responses arise at long timescales. We demonstrate that the viscous response of such anisotropic driven fluids can acquire a tensorial, dissipationless component called anisotropic odd (or Hall) viscosity. Classical fluids with internal torques can display additional components of the odd viscosity neglected in previous studies of quantum Hall fluids that assumed angular momentum conservation. We show that these anisotropic and angular momentum-violating odd-viscosity coefficients can change even the bulk flow of an incompressible fluid by acting as a source of vorticity. In addition, shear distortions in the shape of an inclusion result in torques.