论文标题
阐明耗散量子系统的拓扑
Unraveling the topology of dissipative quantum systems
论文作者
论文摘要
我们从量子轨迹的角度讨论耗散量子系统中的拓扑。后者出现在马尔可夫量子主方程和/或连续量子测量中的揭开中出现。在量子跳跃发生时（即跳跃时间）在出现量子轨迹的一体量轨迹会产生一个离散的，确定性的进化，这对黑暗状态的存在高度敏感。我们为广泛的翻译不变崩溃模型展示了一组诱发黑暗状态的哈密顿人在哈密顿人的空间上施加了非平凡的拓扑结构，这也由相应的Jumptime动力学反映。然后，可以观察到后者的拓扑特征，例如，在运输行为中，可以暴露拓扑相变的无限层次结构。我们开发了一维两波段的哈密顿人的理论，并表明拓扑行为直接体现了手性，PT或时间逆转对称的汉密尔顿人。
We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. The latter emerge in the unraveling of Markovian quantum master equations and/or in continuous quantum measurements. Ensemble-averaging quantum trajectories at the occurrence of quantum jumps, i.e., the jump times, gives rise to a discrete, deterministic evolution which is highly sensitive to the presence of dark states. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians, which is also reflected by the corresponding jumptime dynamics. The topological character of the latter can then be observed, for instance, in the transport behavior, exposing an infinite hierarchy of topological phase transitions. We develop our theory for one- and two-dimensional two-band Hamiltonians and show that the topological behavior is directly manifest for chiral, PT, or time reversal-symmetric Hamiltonians.
