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 characterising 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 the path-integral approach to response in nonequilibrium systems and constrained Gaussian field theory, and they are valid for arbitrary Péclet number. We validate our theoretical results with molecular dynamics simulations of a weakly interacting fluid of rotating active dumbbells.