Floquet states have been used to describe the impact of periodic driving on lattice systems, either using a tight-binding model or by using a continuum model where a Kronig-Penney-like description has been used to model spatially periodic systems in one dimension. A number of these studies have focused on finite systems, and results from these studies are distinct from those of infinite lattice systems as a consequence of boundary effects. In the case of a finite system, there remains a discrepancy in the results between tight-binding descriptions and continuous lattice models. Periodic driving by a time-dependent field in tight-binding models results in a collapse of all quasienergies within a band at special driving amplitudes. In the continuum model, however, a pair of nearly degenerate edge bands emerge and remain gapped from the bulk bands as the field amplitude increases. We resolve these discrepancies and explain how these edge bands represent Schrödinger cat-like states with effective tunneling across the entire lattice. Moreover, we show that these extended cat-like states become perfectly localized at the edge sites when the external driving amplitude induces a collapse of the bulk bands.

中文翻译：

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通过周期性驱动，有限网格中的边缘局部薛定ding猫状态

浮球状态已被用于描述周期性驱动对晶格系统的影响，或者使用紧密绑定模型，或者使用连续模型，其中使用了类似于Kronig-Penney的描述来在一维空间周期性系统中建模。其中许多研究集中在有限系统上，由于边界效应，这些研究的结果与无限晶格系统的结果不同。在有限系统的情况下，紧密绑定描述与连续晶格模型之间的结果仍然存在差异。在紧束缚模型中，由时间相关的场进行的周期性驱动会导致特定驱动幅度下的一个带内的所有准能量崩溃。但是，在连续模型中，随着场振幅的增加，出现了一对几乎简并的边缘带，并与体带保持间隔。我们解决了这些差异，并解释了这些边缘带如何通过整个晶格上的有效隧穿来表示Schrödinger猫状状态。此外，我们显示出，当外部驱动幅度引起体能谱的塌陷时，这些扩展的猫状状态变得完全位于边缘位置。