重复相互作用量子系统：van Hove极限和渐近态
Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States
摘要：
我们建立了重复相互作用的开放量子系统的两个弱耦合区有效动力学的存在性（分别为消失强度和个体相互作用持续时间）。这推广了已知的结果，即描述系统和链元的冯诺依曼代数可能不是有限型的。然后（但现在假设小系统是有限型的），我们证明了这两个有效的动态捕捉系统的长期行为：存在一个独特的渐近状态，他们意味着相同的属性为各自的确切动态-只要扰动参数是足够小的。这种渐近状态的扰动参数的幂级数展开中的零阶项由有效动力学的渐近状态给出。最后，我们计算了小系统和链元都是自旋的情况。
英文摘要：
We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions (vanishing strength and individual interaction duration, respectively). This generalizes known results in that the von Neumann algebras describing the system and the chain element may not be of finite type. Then (but now assuming that the small system is of finite type), we prove that both effective dynamics capture the long-term behaviour of the system: existence of a unique asymptotic state for them implies the same property for the respective exact dynamics--provided that the perturbation parameter is sufficiently small. The zero-th order term in a power series expansion in the perturbation parameter of such an asymptotic state is given by the asymptotic state of the effective dynamics. We conclude by working out the case in which the small system and the chain element are spins.
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