Hall Viscosity

Dissipationless momentum transport in topological fluids

Velocity field with Hall stress

Stress tensor components

σ_xy^H = η_H(∂_xu_x − ∂_yu_y) | η_H = ℏn/2 × s̄

Hall viscosity η_H: 0.5

Shear viscosity η_S: 0.3

Flow type:

Hall viscosity (η_H) is a dissipationless, parity-breaking response present in topological fluids like quantum Hall states, chiral superfluids, and rapidly rotating fluids. Unlike ordinary (shear) viscosity which opposes flow, Hall viscosity rotates the stress tensor by 90°: a shear flow in x generates stress in y. It's quantized in integer/fractional quantum Hall states as η_H = ℏn·s̄/2 where s̄ is the mean orbital spin. Unlike the Hall conductance, it is NOT topologically quantized in general. Avron, Seiler & Zograf (1995) first computed it; Read (2009) connected it to adiabatic Berry phase.