具有集体算符值速率的开放量子系统的量子涨落动力学及其在类Hopfield网络中的应用
Quantum fluctuation dynamics of open quantum systems with collective operator-valued rates, and applications to Hopfield-like networks
AI总结：
该研究针对具有集体算符值速率的GKS-Lindblad型开放量子多体系统，推导无穷大系统极限下的量子涨落算符动力学，并应用于量子广义Hopfield网络，发现介观尺度渐近态仅存在极弱的量子失谐型量子关联。
摘要：
我们研究一类以马尔可夫方式演化的开放量子多体系统，其动力学生成元具有GKS-Lindblad形式。其中，哈密顿量部分的特征是全连接耦合，耗散过程则包含依赖于集体算符值速率的局域跃迁，这类速率编码了系统的平均性质。通过将经典（平均场）随机马尔可夫动力学（含状态依赖跃迁）推广到量子领域，可形式化地得到这类生成元。我们聚焦于系统尺寸趋于无穷大极限下的动力学，基于平均算符动力学的平均场方程的精确性展开研究。在该框架下，我们推导了量子涨落算符的动力学，可用于理解系统中量子关联的演化行为。我们将研究结果应用于量子广义Hopfield联想记忆模型，结果表明：在渐近状态下且仅在介观尺度上，除经典关联外，仅会出现以量子失谐形式存在的极少量量子关联。
英文摘要：
We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the dissipation features local transitions that depend on collective, operator-valued rates, encoding average properties of the system. These types of generators can be formally obtained by generalizing, to the quantum realm, classical (mean-field) stochastic Markov dynamics, with state-dependent transitions. Focusing on the dynamics emerging in the limit of infinitely large systems, we build on the exactness of the mean-field equations for the dynamics of average operators. In this framework, we derive the dynamics of quantum fluctuation operators, that can be used in turn to understand the fate of quantum correlations in the system. We apply our results to quantum generalized Hopfield associative memories, showing that, asymptotically and at the mesoscopic scale only a very weak amount of quantum correlations, in the form of quantum discord, emerges beyond classical correlations.
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