We consider the quantum nonequilibrium dynamics of systems where fermionic particles coherently hop on a one-dimensional lattice and are subject to dissipative processes analogous to those of classical reaction-diffusion models. Particles can either annihilate in pairs, $A+A \to \emptyset$, coagulate upon contact, $A+A \to A$, and possibly also branch, $A \to A+A$. In classical settings, the interplay between these processes and particle diffusion leads to critical dynamics as well as to absorbing state phase transitions. Here, we analyze the impact of coherent hopping and of quantum superposition, focusing on the so-called reaction-limited regime. Here, spatial density fluctuations are quickly smoothed out due to fast hopping, which for classical systems is described by a mean-field approach. By exploiting the time-dependent generalized Gibbs ensemble method, we demonstrate that quantum coherence and destructive interference play a crucial role in these systems and are responsible for the emergence of locally protected dark states and collective behavior beyond mean-field. This can manifest both at stationarity and during the relaxation dynamics. Our results highlight fundamental differences between classical reaction-diffusion dynamics and their quantum counterpart and show that quantum effects indeed change collective universal behavior.

中文翻译：

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反应限制的量子反应扩散动力学

我们考虑系统的量子非平衡动力学，其中费米子粒子相干地在一维晶格上跳跃并受到类似于经典反应扩散模型的耗散过程的影响。粒子可以成对湮灭，$A+A \to \emptyset$，接触时凝固，$A+A \to A$，也可能分支，$A \to A+A$。在经典环境中，这些过程和粒子扩散之间的相互作用导致临界动力学以及吸收状态相变。在这里，我们分析了相干跳跃和量子叠加的影响，重点关注所谓的反应受限状态。在这里，由于快速跳跃，空间密度波动很快就被消除了，这对于经典系统来说是通过平均场方法来描述的。通过利用时间相关的广义吉布斯系综方法，我们证明了量子相干性和相消干涉在这些系统中起着至关重要的作用，并且是造成局部受保护的暗态和平均场之外的集体行为的原因。这可以在平稳性和松弛动力学过程中表现出来。我们的结果突出了经典反应扩散动力学与其量子对应物之间的根本差异，并表明量子效应确实改变了集体普遍行为。这可以在平稳性和松弛动力学过程中表现出来。我们的结果突出了经典反应扩散动力学与其量子对应物之间的根本差异，并表明量子效应确实改变了集体普遍行为。这可以在平稳性和松弛动力学过程中表现出来。我们的结果突出了经典反应扩散动力学与其量子对应物之间的根本差异，并表明量子效应确实改变了集体普遍行为。