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The Physics Department and Center for Theoretical Physics will host a seminar Thursday, October 25 at 12:00 pm in Namm Room 823. Faculty and students are welcome.
Title: Odd surface waves in two-dimensional incompressible fluids
Dr. Sriram Ganeshan
City College of CUNY
New York, NY, USA
In everyday fluids, the viscosity is the measure of resistance to the fluid flow and has a dissipative character. Avron, Seiler, and Zograf showed that viscosity of a quantum Hall (QH) fluid at zero temperature is non-dissipative. This non-dissipative viscosity (also known as ‘odd’ or ‘Hall’ viscosity) is the antisymmetric component of the total viscosity tensor and can be non-zero for parity violating fluids. I will discuss free surface dynamics of a two-dimensional incompressible fluid with the odd viscosity (not quite quantum Hall hydro). For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral. In the limit of vanishing shear viscosity and gravity, we derive effective nonlinear Hamiltonian equations for the surface dynamics, generalizing the linear solutions to the weakly nonlinear case. In a small surface angle approximation, the equation of motion results in a new class of non-linear chiral dynamics which we dub as chiral Burgers equation. I will briefly discuss how this program can be extended to the free surface of quantum Hall hydrodynamics.