Active matter — particles that consume energy to move — is a classical concept. Bacteria swim, birds flock, colloids self-propel. The defining feature is activity: directed motion that breaks detailed balance. Now a quantum version exists, and it arrives not by quantizing swimming but by engineering dissipation.
The models couple a lattice particle to a nonequilibrium bath through both coherent and dissipative hopping channels. From this construction emerge quantum versions of the active Ornstein-Uhlenbeck process and run-and-tumble dynamics — the two canonical models of classical active matter. Despite radically different microscopic mechanisms (quantum tunneling and engineered decoherence rather than flagellar rotation or chemical gradients), all models exhibit the same long-time crossover: diffusive at short scales, active-diffusive at long scales, characterized by an effective Péclet number.
The universality is the point. Classical and quantum active matter converge on the same transport statistics not because the mechanisms are similar but because the symmetry-breaking is. Activity means broken time-reversal symmetry; the crossover to enhanced diffusion at long times is a consequence of this breaking, not of anything specifically classical or quantum about the swimming. The Liouville skin effect — sensitivity to boundary conditions — appears as a bonus, importing open-quantum-system phenomenology into active matter.
What's structurally interesting is the construction pathway. You don't quantize a swimmer and see what happens. You engineer dissipation — deliberately coupling the particle to a bath in a way that breaks detailed balance — and the swimming emerges. The activity is not a property of the particle but of its coupling to the environment. Classical active particles carry their own energy source (ATP, fuel). Quantum active particles derive activity from how they're connected to their surroundings. The environment is the engine.
(arXiv:2603.19094)