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

Gerbino, Federico; Lesanovsky, Igor; Perfetto, Gabriele

Abstract

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.

Citation

Gerbino, F., Lesanovsky, I., & Perfetto, G. (2024). Large-scale universality in quantum reaction-diffusion from Keldysh field theory. Physical Review B, 109(22), Article L220304. https://doi.org/10.1103/physrevb.109.l220304

• Journal Article Type: Article
• Acceptance Date: May 30, 2024
• Online Publication Date: Jun 24, 2024
• Publication Date: Jun 1, 2024
• Deposit Date: Jul 22, 2024
• Journal: Physical Review B
• Print ISSN: 2469-9950
• Electronic ISSN: 2469-9969
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 109
• Issue: 22
• Article Number: L220304
• DOI: https://doi.org/10.1103/physrevb.109.l220304
• Public URL: https://nottingham-repository.worktribe.com/output/36579910
• Publisher URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.L220304