  Along a microtubule, certain active motors propel themselves in one direction
whereas others propel themselves in the opposite direction. For example, the
cargo transporting motor proteins dynein and kinesin propel themselves towards
the so-called plus- and minus-ends of the microtubule, respectively, and in so
doing are able to pass one another, but not without interacting. We address the
emergent collective behavior of systems composed of many motors, some
propelling towards the plus-end and others propelling towards the minus-end. To
do this, we used an analogy between this strongly interacting,
far-from-equilibrium, classical stochastic many-motor system and a certain
quantum-mechanical many-body system evolving in imaginary time. We apply
well-known methods from quantum many-body theory, including self-consistent
mean-field theory and bosonization, to shed light on phenomena exhibited by the
many-motor system such as structure formation and the dynamics of collective
modes at low-frequencies and long-wavelengths. In particular, via the bosonized
description we find analogs of chiral Luttinger liquids, as well as a
qualitative transition in the nature of the low-frequency modes---from
propagating to purely dissipative---controlled by density and interaction
strength.
