(53l) Breakdown of the Stokes-Einstein Relation for a Passive Tracer in an Odd-Viscous Chiral Active Fluid

Isotropic Newtonian fluids in two-dimensions may in general exhibit both the typical viscous shear response as well as a so-called odd viscosity, which couples forcing to flow in an orthogonal direction. This anti-symmetry reflects the breaking of microscopic time-reversal symmetry, either due to activity of the constituent particles or the presence of an external magnetic field. Passive tracer particles suspended in odd-viscous fluids experience an anomalous lift force when subjected to a constant velocity, corresponding to non-vanishing off-diagonal components of the mobility tensor and the breakdown of the Stokes-Einstein relation. We present theoretical results characterizing the odd-viscous response in active chiral fluids and the mobility tensor of a passive tracer suspended in a such a fluid. Our analytical results are derived using a combination of a stochastic Irving-Kirkwood procedure, used to derive the odd-viscous hydrodynamic equations, and the path-integral approach to response in active systems, which allows us to derive generalized Green-Kubo expressions for the relevant viscosities and tracer mobility tensor that are valid for arbitrary Péclet number. We validate our results via molecular dynamics simulation of a chiral active fluid. In addition to elucidating the application of recently developed techniques in nonequilibrium response theory, we demonstrate the possibility of size-dependent particle separation in odd-viscous fluids.