Resolving Hall and dissipative viscosity ambiguities via boundary effects

Abstract

We examine in detail the ambiguity of viscosity coefficients in two-dimensional anisotropic fluids emphasized in [Rao and Bradlyn, Phys. Rev. X 10, 021005 (2020)], where it was shown that different components of the dissipative and non-dissipative (Hall) viscosity tensor correspond to physically identical effects in the bulk. Considering fluid flow in systems with a boundary, we are able to distinguish between the otherwise redundant viscosity components, and see the effect of the "contact terms" (divergenceless contributions to the stress tensor) that shift between them. We show how the dispersion and damping of gravity-dominated surface waves can be used to disambiguate respectively between redundant Hall and dissipative viscosity coeffients. We discuss how these results apply to recent experiments in chiral active fluids with nonvanishing Hall viscosity. Finally, we apply our results to the hydrodynamics of the quantum Hall fluid, and show that the boundary term that renders the bulk Wen-Zee action nonanomalous can be reinterpreted in terms of the bulk viscous redundancy.

Hydrodynamics with triangular point group

“…We have presented the hydrodynamics of a two-dimensional fluid with D 6 point group. In contrast to earlier works which focus on the viscosity tensor [16][17][18][19][20][21], we have additionally found a new dissipative coefficient, α (and its Onsager partner β), which is allowed by the explicit breaking of spatial-inversion and time-reversal symmetries.…”

“…Here we consider the hydrodynamics of an anisotropic electron fluid; with only a handful of exceptions [16][17][18][19][20][21], most of the theoretical literature on electron hydrodynamics is restricted to isotropic liquids [22][23][24][25][26][27][28][29][30], which have continuous rotational invariance. However, in fluids with a discrete (finite) rotational point group, one may realize hydrodynamic phenomena not possible with continuous rotational invariance.…”

Hydrodynamic effective field theories with discrete rotational symmetry

“…On the other hand, the symmetric part of the viscosity tensor is relatively stable against rotational symmetry breaking (see a thorough group theory discussion in [35,36]). More generally, for even N , the viscosity tensor of a D N ≥6 -invariant fluid looks just like an O(2)-invariant fluid, up to the rotational viscosity η • (which is nearly invisible in simple fluid flow experiments [36,71]); while for D N ≤4 , anisotropy appears in the symmetric viscosity as shown in (4.34). However, this is not true for odd N as discussed below.…”

Hydrodynamic effective field theories with discrete rotational symmetry

“…On the other hand, the symmetric part of the viscosity tensor is relatively stable against rotational symmetry breaking (see a thorough group theory discussion in [35,36]). More generally, for even N , the viscosity tensor of a D N ≥6 -invariant fluid looks just like an O(2)invariant fluid, up to the rotational viscosity η • (which is nearly invisible in simple fluid flow experiments [36,68]); while for D N ≤4 , anisotropy appears in the symmetric viscosity as shown in (4.34). However, this is not true for odd N as discussed below.…”