论文标题
赫尔米尼亚和非铁量量子力学中的新兴平行运输和曲率
Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
论文作者
论文摘要
研究表明，非省系统的希尔伯特空间需要非平凡的指标。在这里，我们证明了进化维度除了时间之外，还可以从几何形式主义中自然出现。具体而言，在这种形式主义中，哈密顿人可以被解释为类似于基督教的符号的操作员，而施罗丁格方程式是这种形式主义的平行运输。然后，我们得出了沿紧急尺寸的状态和指标的演化方程，发现希尔伯特空间束的曲率对于任何给定的封闭系统都是局部平坦的。最后，我们表明，国家的富裕性敏感性和浆果曲率与这些新兴平行运输有关。
Studies have shown that the Hilbert spaces of non-Hermitian systems require nontrivial metrics. Here, we demonstrate how evolution dimensions, in addition to time, can emerge naturally from a geometric formalism. Specifically, in this formalism, Hamiltonians can be interpreted as a Christoffel symbol-like operators, and the Schroedinger equation as a parallel transport in this formalism. We then derive the evolution equations for the states and metrics along the emergent dimensions and find that the curvature of the Hilbert space bundle for any given closed system is locally flat. Finally, we show that the fidelity susceptibilities and the Berry curvatures of states are related to these emergent parallel transports.
