ZhETF, Vol. 144,
p. 617 (September 2013)
(English translation - JETP,
Vol. 117, No. 3,
available online at www.springer.com
ANOMALOUS HYDRODYNAMICS OF FRACTIONAL QUANTUM HALL STATES
Received: May 16, 2013
Dedicated to the memory of Professor Anatoly Larkin} We propose a comprehensive framework for quantum hydrodynamics of the fractional quantum Hall (FQH) states. We suggest that the electronic fluid in the FQH regime can be phenomenologically described by the quantized hydrodynamics of vortices in an incompressible rotating liquid. We demonstrate that such hydrodynamics captures all major features of FQH states, including the subtle effect of the Lorentz shear stress. We present a consistent quantization of the hydrodynamics of an incompressible fluid, providing a powerful framework to study the FQH effect and superfluids. We obtain the quantum hydrodynamics of the vortex flow by quantizing the Kirchhoff equations for vortex dynamics.