Hydrodynamics of the fractional quantum Hall effect (Vol. 44 No. 6)

Many features of the Fractional Quantum Hall effect (FQHE) can be understood by considering electrons on the surface of semiconductors as a very peculiar, charged, two-dimensional fluid in the presence of a strong magnetic field. In this paper a classical hydrodynamic model of such a fluid is presented.

The model incorporates a relation between the vorticity and density of the fluid specific for FQHE and exhibits the Hall viscosity and Hall conductivity found in FQHE liquids. The relation of the model to previous effective models such as the Chern–Simons–Ginzburg– Landau theory of FQHE is explained. It is also shown how the Laughlin’s wavefunction is annihilated by the quantum velocity operator.