Hydrodynamics of Euler incompressible fluid and the fractional quantum Hall effect

We show that the fractional quantum Hall effect can be phenomenologically described as a special flow of a quantum incompressible Euler liquid. This flow consists of a large number of vortices of the same chirality. In this approach each vortex is identified with an electron while the fluid is neutral. We show that the Laughlin wave function naturally emerges as a stationary flow of the system of vortices in quantum fluid dynamics. Here we develop the hydrodynamics of the vortex liquid and are able to consistently quantize it. As a demonstration of the efficiency of the hydrodynamics we show how subtle features of the fractional quantum Hall effect such as effects of Lorentz shear stress, the structure function, the Hall current in a nonuniform magnetic field, and Hall conductance in a curved spatial landscape naturally follow from the hydrodynamics approach.