论文标题
变异方法的几何形状：封闭量子系统的动力学
Geometry of variational methods: dynamics of closed quantum systems
论文作者
论文摘要
我们提出了一个系统的几何框架，用于研究基于适当选择的变异家庭的封闭量子系统。出于（a）实时演变的目的，（b）激发光谱，（c）光谱函数和（d）假想时间的演变，我们展示了几何方法如何突出有必要区分两类的流形：kähler和non-kähhler。传统的变分方法通常要求变分家族为Kähler歧管，其中通过假想单元的乘法保留了切线空间。这涵盖了文献中研究的绝大多数案例。但是，最近提议的一类普遍高斯州的类别使得还必须包括偶尔遇到的非kähler案。我们用一系列具体示例详细说明了我们的方法，其中所考虑的歧管的几何结构特别相关。这些从高斯州和理论相干国家转变为普遍的高斯州。
We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kähler and non-Kähler. Traditional variational methods typically require the variational family to be a Kähler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-Kähler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.
