绝热Floquet理论中的几何相位、阿贝尔gerbes和Cheon的非完整性
Geometric phases in adiabatic Floquet theory, abelian gerbes and Cheon's anholonomy
摘要：
我们研究的背景下的绝热Floquet理论（所谓的$(t,t')$ Floquet理论）的几何相位现象。由于理论中存在两个时间变量，几何相位公式中出现了双重积分。我们表明，几何相位，然后确定与水平升降机的表面在一个阿贝尔gerbe的连接，而不是与水平升降机的曲线在一个阿贝尔主丛。几何相位规范理论中的这种更高程度与参数流形的两个局部图之间的过渡处的Floquet块中的变化的外观有关。我们提出了一个踢两级系统的物理例子，这些变化涉及通过千的anholonomy。在这方面，通常的几何相理论与经典场论之间的类比也提供了与经典弦论的类比。
英文摘要：
We study the geometric phase phenomenon in the context of the adiabatic Floquet theory (the so-called the $(t,t')$ Floquet theory). A double integration appears in the geometric phase formula because of the presence of two time variables within the theory. We show that the geometric phases are then identified with horizontal lifts of surfaces in an abelian gerbe with connection, rather than with horizontal lifts of curves in an abelian principal bundle. This higher degree in the geometric phase gauge theory is related to the appearance of changes in the Floquet blocks at the transitions between two local charts of the parameter manifold. We present the physical example of a kicked two-level system where these changes are involved via a Cheon's anholonomy. In this context, the analogy between the usual geometric phase theory and the classical field theory also provides an analogy with the classical string theory.
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