  Active liquid crystals exert nonequilibrium stresses on their surroundings
through constant consumption of energy, giving rise to dynamical steady states
not present in equilibrium. The paradigmatic example of an active liquid
crystal is a suspension of microtubule bundles powered by kinesin motor
proteins, which exhibits self-sustained spatiotemporal chaotic flows. This
system has been modelled using continuum theories that couple the microtubule
orientation to active flows. Recently the focus has shifted to the interfacial
properties of mixtures of active liquid crystals and passive fluids.
Active/passive interfaces have been shown to support propagating capillary
waves in the absence of inertia and offer a promising route for relating
experimental parameters to those of the continuum theory. In this paper we
report the derivation of a minimal model that captures the linear dynamics of
the interface between an active liquid crystal and a passive fluid. We show
that the dynamics of the interface, although powered by active flows throughout
the bulk, is qualitatively captured by equations that couple non-reciprocally
interface height and nematic director at the interface. This minimal model
reproduces the dynamical structure factor evaluated from numerical simulations
and the qualitative form of the wave dispersion relation seen in experiments.
