Helical Hydrodynamics

Normal fluids like water and air are described by the famous Navier-Stokes Equations, which apply to any system that respects Galileo symmetry. However, when the symmetry group is more exotic, novel terms may modify the NS equations and lead to interesting behaviour. For Farrell, Huang, Lucas (2022), we investigated a fluid with the symmetry of a helix: only the combination $\ P_z + L_z/\xi\ $ is a conserved quantity, not $\ P_z$ or $\ L_z \ $ separately. Interestingly, the transport coefficients of the helical theory are partially fixed by symmetry alone, and the fluid also features transverse responses, for example supplying a torque in the presence of a uniform electric field!

The figure is a cartoon illustrating helical symmetry.

Dyakonov-Shur Instability in an Annulus

In very clean samples, electrons can flow like a liquid. For Farrell, Grisouard, Scaffidi (2021), I used a finite-volume method to simulate a viscous electron gas flowing radially in a ring. With certain boundary conditions, this setup experiences an instability: small perturbations to the steady state grow and oscillate at a certain frequency. Depending on the length of the channel, this frequency can reach the range of TeraHertz, a region of the electromagnetic spectrum for which few good sources or detectors currently exist!

The figure shows the instability’s growth rate and frequency as functions of the bias current in the radial direction.