The cooperation between time-periodic driving fields and non-Hermitian effects could endow systems with distinctive spectral and transport properties. In this paper, we uncover an intriguing class of non-Hermitian Floquet matter in one-dimensional quasicrystals, which is characterized by the emergence of multiple driving-induced $\mathcal{PT}$-symmetry breaking/restoring transitions, mobility edges, and reentrant localization transitions. These findings are demonstrated by investigating the spectra, level statistics, inverse participation ratios, and wave-packet dynamics of a periodically quenched nonreciprocal Harper model. Our results not only unveil the richness of localization phenomena in driven non-Hermitian quasicrystals but also highlight the advantage of the Floquet approach in generating unique types of nonequilibrium phases in open systems.

中文翻译：

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非 Hermitian Floquet 准晶体中驱动诱导的多重 PT 对称破坏跃迁和重入定位跃迁

时间周期驱动场和非厄米特效应之间的合作可以赋予系统独特的光谱和传输特性。在本文中，我们在一维准晶体中发现了一类有趣的非厄米特 Floquet 物质，其特征是出现了多重驱动诱导$\mathcal{PT}$-对称破坏/恢复转换、移动边缘和可重入定位转换。这些发现通过研究周期性淬火非互易 Harper 模型的光谱、水平统计、逆参与比和波包动力学来证明。我们的结果不仅揭示了驱动非厄米特准晶体中定位现象的丰富性，而且突出了 Floquet 方法在开放系统中生成独特类型的非平衡相方面的优势。