标题： 开放量子系统的集体算子速率的量子涨落动力学及其在类似Hopfield网络中的应用 显示英文标题

标题： Quantum fluctuation dynamics of open quantum systems with collective operator-valued rates, and applications to Hopfield-like networks

摘要： 我们考虑一类以马尔可夫方式演化的开放量子多体系统，其动力学生成元以GKS-Lindblad形式存在。在这里，哈密顿量贡献由全连接耦合表征，耗散特征是依赖于集体、算符值速率的局部跃迁，这些速率编码了系统的平均性质。这类生成元可以通过将经典的（平均场）随机马尔可夫动力学推广到量子领域来形式地获得，其中状态依赖的跃迁存在。专注于无限大系统极限下出现的动力学，我们利用平均场方程对平均算符动力学的精确性。在此框架中，我们推导了量子涨落算符的动力学，这些动力学可以用来理解系统中量子关联的命运。我们将结果应用于量子广义霍普菲尔德联想记忆，表明在渐近情况下且仅在介观尺度上，除了经典关联外，仅有非常少量的量子关联以量子失谐的形式出现。 显示英文摘要

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.