Hall Viscosity — Topological Fluid

Hall (odd) viscosity η_H is a parity-breaking viscous coefficient: stress is rotated 90° from the strain rate. For the ν=1/2 Laughlin state: η_H = nℏ/4. Watch how shear drives perpendicular flow.

σᵢⱼ = 2η ε̇ᵢⱼ + 2η_H ε̃̇ᵢⱼ
ε̃̇ᵢⱼ = ½(εᵢₖεₖⱼ + εⱼₖεₖᵢ) [90° rotation]

Normal: σₓᵧ = 2η ε̇ₓᵧ
Hall: σₓₓ − σᵧᵧ = 4η_H ε̇ₓᵧ

For ν=1/2 FQH:
η_H = nℏ/4 (quantized!)
normal stress σₓₓ
Hall stress σᵧᵧ
velocity field
Stress components vs time — Hall stress is 90° phase-shifted