Large-scale universality in quantum reaction-diffusion from Keldysh field theory

We consider the quantum reaction-diffusion dynamics in d spatial dimensions of a Fermi gas subject to binary annihilation reactions A+A. These systems display collective nonequilibrium long-time behavior, which is signalled by an algebraic decay of the particle density. Building on the Keldysh formalism, we devise a field theoretical approach for the reaction-limited regime, where annihilation reactions are scarce. Combining a perturbative expansion of the dissipative interaction with Euler-hydrodynamic scaling limit, we derive a description in terms of a large-scale universal kinetic equation. Our approach shows how the time-dependent generalized Gibbs ensemble assumption, which is often employed for treating low-dimensional nonequilibrium dissipative systems, emerges from systematic diagrammatics. It also allows us to exactly compute---for arbitrary spatial dimension---the decay exponent of the particle density. The latter is based on the large-scale description of the quantum dynamics and it differs from the mean-field prediction even in dimension larger than one. We moreover consider spatially inhomogeneous setups involving an external potential. In confined systems the density decay is accelerated towards the mean-field algebraic behavior, while for deconfined scenarios the power-law decay is replaced by a slower nonalgebraic decay.