Quantum reaction-limited reaction-diffusion dynamics of annihilation processes

Perfetto, Gabriele; Carollo, Federico; Garrahan, Juan P; Lesanovsky, Igor

Abstract

We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice and undergo annihilation reactions. The latter are modelled as dissipative processes which involve losses of pairs 2A→∅, triplets 3A→∅, and quadruplets 4A→∅ of neighboring particles. When considering classical particles, the corresponding decay of their density in time follows an asymptotic power-law behavior. The associated exponent in one dimension is different from the mean-field prediction whenever diffusive mixing is not too strong and spatial correlations are relevant. This specifically applies to 2A→∅, while the mean-field power-law prediction just acquires a logarithmic correction for 3A→∅ and is exact for 4A→∅. A mean-field approach is also valid, for all the three processes, when the diffusive mixing is strong, i.e., in the so-called reaction-limited regime. Here we show that the picture is different for quantum systems. We consider the quantum reaction-limited regime and we show that for all the three processes power-law behavior beyond mean field is present as a consequence of quantum coherences, which are not related to space dimensionality. The decay in 3A→∅ is further, highly intricate, since the power-law behavior therein only appears within an intermediate time window, while at long times the density decay is not power law. Our results show that emergent critical behavior in quantum dynamics has a markedly different origin, based on quantum coherences, to that applying to classical critical phenomena, which is, instead, solely determined by the relevance of spatial correlations.

Citation

Perfetto, G., Carollo, F., Garrahan, J. P., & Lesanovsky, I. (2023). Quantum reaction-limited reaction-diffusion dynamics of annihilation processes. Physical Review E, 108(6), Article 064104. https://doi.org/10.1103/physreve.108.064104

• Journal Article Type: Article
• Acceptance Date: Oct 23, 2023
• Online Publication Date: Dec 4, 2023
• Publication Date: 2023-12
• Deposit Date: Jan 22, 2024
• Publicly Available Date: Jan 23, 2024
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 108
• Issue: 6
• Article Number: 064104
• DOI: https://doi.org/10.1103/physreve.108.064104
• Keywords: Nonequilibrium statistical mechanics; Quantum statistical mechanics; Reaction diffusion systems; Kinetically constrained models; Lindblad equation; Master equation
• Public URL: https://nottingham-repository.worktribe.com/output/28152735
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.064104