标题： 量子前兆在弗洛凯自旋-$J$系统中的柯尔莫戈罗夫-阿诺德-莫泽定理 显示英文标题

标题： Quantum precursors to Kolmogorov-Arnold-Moser theorem in Floquet spin-$J$ systems

摘要： KAM定理证明，当引入非可积扰动时，经典可积哈密顿系统的共振环面会被破坏，而非共振环面仅在扰动参数达到有限值之前发生形变。 在本简报中，我们识别了一维自由度自旋哈密顿系统在周期性瞬时扰动下的量子前兆。 在认识到受扰哈密顿系统的弗洛凯本征态中的共振量子特征后，我们揭示了未受扰哈密顿本征态对扰动的不同敏感性，这取决于这些态是否满足共振条件。 还表明，随着系统尺寸的增加，这种不同的敏感性变得更加明显，从而在经典极限$J\rightarrow\infty$中导致KAM定理。 从幺正扰动理论中获得的数值和分析结果强烈支持这些发现。 尽管特定于踢模型，我们的结果可以轻松扩展到更一般的情况，从而能够识别对应于经典极限中KAM定理的量子机制。 显示英文摘要

摘要： The Kolmogorov-Arnold-Moser (KAM) theorem proves that the resonant tori of classical integrable Hamiltonians are broken when a non-integrable perturbation is introduced, whereas non-resonant tori only get deformed for up to a finite value of the perturbative parameter. In this letter, we identify quantum precursors to the KAM theorem in one-degree-of-freedom spin Hamiltonians periodically perturbed by instantaneous kicks. After recognizing quantum signatures of resonances in the Floquet eigenstates of the perturbed Hamiltonian, we reveal a differentiated sensitivity to the perturbation of the eigenstates of the unperturbed Hamiltonian, depending on whether the states satisfy a resonant condition or not. It is also shown that this differentiated sensitivity becomes more pronounced as the system size increases, leading to the KAM theorem in the classical limit $J\rightarrow\infty$. Numerical and analytical results obtained from unitary perturbation theory strongly support these findings. Although specific to kicked models, our results can be easily extended to more general scenarios, allowing the identification of the quantum mechanism that corresponds to the KAM theorem in the classical limit.