Anomalous hydrodynamics in two dimensions. Quantum Hall and Vortex fluids.
Thu, Dec. 19th 2013, 14:15-15:15
In the absence of time-reversal symmetry two-dimensional isotropic fluids can have anomalous corrections to stress tensor proportional to velocity gradients even in the absence of dissipation.
I will consider two examples of such fluids. The first one is the Fractional Quantum Hall Effect (FQHE).
In FQHE the electrons on surfaces of semiconductors can be considered as a very peculiar, charged, two-dimensional fluid in the presence of strong magnetic field. I will present a classical hydrodynamic model of such a fluid. The model incorporates the relation between the vorticity and density of the fluid specific for FQHE and exhibits the Hall conductivity and the anomalous stress known as Hall viscosity. In the second example the anomalous stress appears in the effective description of quantized vortices in conventional hydrodynamics of incompressible liquid governed by Euler equations. We develop this hydrodynamics of vortex fluid. The origin of the anomalous stresses in the vortex fluid is a divergence of inter-vortex interactions at the micro-scale which manifests at the macro-scale. We obtain the hydrodynamics of the vortex fluid from the Kirchhoff equations for dynamics of point-like vortices and discuss some consequences of anomalous stresses.