论文标题
有限维量子系统中保守量的KAM稳定性
KAM-Stability for Conserved Quantities in Finite-Dimensional Quantum Systems
论文作者
论文摘要
我们表明，对于任何有限维量子系统，保守的量可以以对小扰动的稳健性来表征：对于脆弱的对称性，小扰动可能会导致长时间的较大偏差，而对于稳健的对称性，他们的期望值一直接近其所有时间的初始值。这与著名的Kolmogorov-Arnold-Moser（KAM）定理相比。为了证明这一非凡的结果，我们引入了扰动系列的重新介绍，该系列概括了量子Zeno动力学的哈密顿量。
We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries small perturbations can lead to large deviations over long times, while for robust symmetries their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser (KAM) theorem in classical mechanics. To prove this remarkable result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.
