Quantum reaction-limited reaction-diffusion dynamics of annihilation processes

• URL: http://arxiv.org/abs/2305.06944v2
• Date: Thu, 28 Dec 2023 18:35:14 GMT
• Title: Quantum reaction-limited reaction-diffusion dynamics of annihilation processes
• Authors: Gabriele Perfetto, Federico Carollo, Juan P. Garrahan, Igor Lesanovsky
• Abstract summary: We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice. The resulting dissipative processes involve losses of pairs $2A to emptyset$, triplets $3A to emptyset$, and quadruplets $4A to emptyset$ of neighbouring particles.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $2A \to \emptyset$, triplets $3A \to \emptyset$, and quadruplets $4A \to \emptyset$ of neighbouring 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 $2A\to \emptyset$, while the mean-field power-law prediction just acquires a logarithmic correction for $3A \to \emptyset$ and is exact for $4A \to \emptyset$. 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 $3A\to \emptyset$ 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.

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