标题： 周期性和非周期性Thue-Morse驱动的长程系统：从动力学局域化到慢动力学 显示英文标题

标题： Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics

摘要： 我们研究了电场驱动的幂律随机带状矩阵(PLRBM)模型，其中幂律指数$\alpha$的变化会导致从局域化到非局域化的相变。 我们借助弗洛凯算符检查了周期驱动的PLRBM模型。 弗洛凯哈密顿量的能级间距比和广义参与比揭示了由驱动引起的分形相，在未驱动的PLRBM模型的非局域化一侧伴随着扩散输运。 在局域化一侧，时间周期模型保持局域化——平均间距比对应于泊松统计，并在动力学中观察到对数输运。 将我们的分析扩展到非周期性的塔克-莫尔斯(TM)驱动系统，我们发现非周期性驱动的干净长程跃迁模型（PLRBM模型的干净对应物）在调节驱动参数到特殊点时表现出\textit{精确动力学局域化}（EDL）现象。 无序的时间非周期系统在非局域化一侧表现出扩散输运，随后弛豫到无限温度态，在局域化一侧则表现出预热平台并伴随亚扩散。 此外，我们将它与一个也经历局域化-非局域化相变的准周期驱动AAH模型进行了比较。 与无序的长程模型不同，即使在非局域化一侧，它也表现出延长的预热平台，随后是向无限温度态的亚扩散。 显示英文摘要

摘要： We investigate the electric-field driven power-law random banded matrix(PLRBM) model where a variation in the power-law exponent $\alpha$ yields a delocalization-to-localization phase transition. We examine the periodically driven PLRBM model with the help of the Floquet operator. The level spacing ratio and the generalized participation ratio of the Floquet Hamiltonian reveal a drive-induced fractal phase accompanied by diffusive transport on the delocalized side of the undriven PLRBM model. On the localized side, the time-periodic model remains localized - the average spacing ratio corresponds to Poisson statistics and logarithmic transport is observed in the dynamics. Extending our analysis to the aperiodic Thue-Morse (TM) driven system, we find that the aperiodically driven clean long-range hopping model (clean counterpart of the PLRBM model) exhibits the phenomenon of \textit{exact dynamical localization} (EDL) on tuning the drive-parameters at special points. The disordered time-aperiodic system shows diffusive transport followed by relaxation to the infinite-temperature state on the delocalized side, and a prethermal plateau with subdiffusion on the localized side. Additionally, we compare this with a quasi-periodically driven AAH model that also undergoes a localization-delocalization transition. Unlike the disordered long-range model, it features a prolonged prethermal plateau followed by subdiffusion to the infinite temperature state, even on the delocalized side.