Resolving Hall and dissipative viscosity ambiguities via boundary effects

Abstract

We examine the physical implications of the viscous redundancy of two-dimensional anisotropic fluids, where different components of the viscosity tensor lead to identical effects in the bulk of a system [Rao and Bradlyn, Phys. Rev. X $\textbf{10}$, 021005 (2020)]. We first re-introduce the redundancy, show how it reflects a lack of knowledge of microscopic information of a system, and give microscopic examples. Next, we show that fluid flow in systems with a boundary can distinguish between otherwise redundant viscosity coefficients. In particular, we show how the dispersion and damping of gravity-dominated surface waves can be used to resolve the redundancies between both dissipative and Hall viscosities, and discuss how these results apply to recent experiments in chiral active fluids with nonvanishing Hall viscosity. Our results highlight the importance of divergenceless, magnetization-like contributions to the stress (which we dub ``contact terms''). Finally, we apply our results to the hydrodynamics of quantum Hall fluids, and show that the extra contribution to the action that renders the bulk Wen-Zee action gauge invariant in systems with a boundary can be reinterpreted in terms of the bulk viscous redundancy.