Generalized Landau levels are harmonic maps, and the Hall viscosity of the nth generalized Landau level is quantized to (2n+1) times the lowest-level value, matching ordinary Landau levels.
Viscosity of Quantum Hall Fluids
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The viscosity of quantum fluids with an energy gap at zero temperature is non-dissipative and is related to the adiabatic curvature on the space of flat background metrics (which plays the role of the parameter space). For a quantum Hall fluid on two dimensional tori this viscosity is computed. In this case the average viscosity is quantized and is proportional to the total magnetic flux through the torus.
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Geometrical Responses of Generalized Landau Levels: Structure Factor and the Quantized Hall Viscosity
Generalized Landau levels are harmonic maps, and the Hall viscosity of the nth generalized Landau level is quantized to (2n+1) times the lowest-level value, matching ordinary Landau levels.