论文标题
非马克维亚耗散量子步行的拓扑过渡
Topological transition of a non-Markovian dissipative quantum walk
论文作者
论文摘要
我们在su-schrieffer-heeger（SSH）晶格上扩展了非热拓扑量子步行[M. S. Rudner和L. Levitov，物理。莱特牧师。 102，065703（2009）]非马克维亚进化的情况。通过将SSH晶格中的每个单元与由准级别形成的储层中的每个单位电池耦合来建立这种非马克维亚模型。即使在非马克维亚进化论的情况下，我们也会发现该模型中的拓扑过渡，沃克可能会在此访问水库并稍后返回SSH晶格。但是，拓扑转换的存在确实取决于储层的低频特性，其特征是光谱密度$ j（ε）\ propto |ε|^α$。特别是，我们发现了亚欧姆（$α<1 $）和欧姆（$α= 1 $）储层的强大拓扑过渡，但没有超级欧摩（$α> 1 $）储层的拓扑过渡。这种行为与自旋 - 玻色子模型的众所周知的定位过渡直接相关。我们通过明确评估该模型的马克维亚性度量来确认非马克维亚动力学的存在。
We extend non-Hermitian topological quantum walks on a Su-Schrieffer-Heeger (SSH) lattice [M. S. Rudner and L. Levitov, Phys. Rev. Lett. 102, 065703 (2009)] to the case of non-Markovian evolution. This non-Markovian model is established by coupling each unit cell in the SSH lattice to a reservoir formed by a quasi-continuum of levels. We find a topological transition in this model even in the case of non-Markovian evolution, where the walker may visit the reservoir and return to the SSH lattice at a later time. The existence of a topological transition does, however, depend on the low-frequency properties of the reservoir, characterized by a spectral density $J(ε)\propto |ε|^α$. In particular, we find a robust topological transition for a sub-Ohmic ($α<1$) and Ohmic ($α=1$) reservoir, but no topological transition for a super-Ohmic ($α>1$) reservoir. This behavior is directly related to the well-known localization transition for the spin-boson model. We confirm the presence of non-Markovian dynamics by explicitly evaluating a measure of Markovianity for this model.
