Abstract

From the stagnant flow of honey to the drag forces on a ball in air, nature provides many examples of viscosity, which dissipates power and slows things down. In some exotic classical and quantum fluids, there are also “Hall” viscosities, components of viscosity that do not dissipate power, instead providing forces transverse to fluid motion. However, the standard approach to hydrodynamics assumes rotational symmetry, which is absent in many electron fluids. In this talk, we examine the non-dissipative Hall viscosity in systems with both discrete symmetry (translational & rotational) and internal degrees of freedom. We first examine the rotational symmetry breaking components of the Hall viscosity in systems with point group symmetry, with a focus on the hydrodynamic implications of the resulting forces. We find that though there are generally six Hall viscosities, there are only three independent contributions to the viscous force density. To compute these coefficients, we develop a framework to consistently define the long-wavelength stress and viscosity tensors for multi-component lattice and continuum systems, emphasizing the importance of internal angular momentum. We conclude by applying our formalism to several example topological systems both on the lattice and in the continuum.