2018/05/29 by Fei-Lei Xiong, Zeng‐Bing Chen, Xiong, Fei-Lei +1
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1805.11330
In the theory of open quantum systems, divisibility of the system dynamical maps is related to memory effects in the dynamics. By decomposing the system Hilbert space as a direct sum of several Hilbert spaces, we study the relationship among the corresponding dynamical maps. It is shown that if the dynamical maps of the open system possess a chain of invariant subspaces, there exists a divisibility hierarchy for their corresponding dynamics. Two classes of examples are given for illustrating these hierarchical structures. One is the pure-dephasing dynamics, and the other is the decay dynamics. Our results offer a systematic approach to obtaining the divisibility conditions and non-Markovian witnesses for these dynamics. Moreover, as a new way of decomposing open quantum systems, it is worthy of further study.