  ATP-driven microtubule-kinesin bundles can self-assemble into two-dimensional
active liquid crystals (ALCs) that exhibit a rich creation and annihilation
dynamics of topological defects, reminiscent of particle-pair production
processes in quantum systems. This recent discovery has sparked considerable
interest but a quantitative theoretical description is still lacking. We
present and validate a minimal continuum theory for this new class of active
matter systems by generalizing the classical Landau-de Gennes free-energy to
account for the experimentally observed spontaneous buckling of motor-driven
extensile microtubule bundles. The resulting model agrees with recently
published data and predicts a regime of antipolar order. Our analysis implies
that ALCs are governed by the same generic ordering principles that determine
the non-equilibrium dynamics of dense bacterial suspensions and elastic bilayer
materials. Moreover, the theory manifests an energetic analogy with strongly
interacting quantum gases. Generally, our results suggest that complex
non-equilibrium pattern-formation phenomena might be predictable from a few
fundamental symmetry-breaking and scale-selection principles.
