标题： 时变量子几何张量及其一些应用 显示英文标题

标题： Time-dependent quantum geometric tensor and some applications

摘要： 我们定义了一个时间相关的量子几何张量扩展，通过考虑时间和波函数参数的小变化，来描述量子态的时间参数空间的几何结构。 与标准量子几何张量相比，这个张量引入了新的时间分量，使得能够分析非时间可分离或显式时间依赖的量子态系统，并编码这些系统的更多信息。 特别是，该张量的时间-时间分量与系统的能量色散有关。 我们将这一框架应用于简谐/倒置振子、时间依赖的简谐振子以及一组广义简谐/倒置振子。 我们展示了与时间依赖的量子几何张量相关的标量曲率的一些结果，以及在从简谐振子到倒置振子转变过程中广义贝里曲率的行为。 此外，我们通过纯度分析研究了链的纠缠，在所述转变中得出任何激发态的纯度都为零。 显示英文摘要

摘要： We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the standard quantum geometric tensor, this tensor introduces new temporal components, enabling the analysis of systems with non-time-separable or explicitly time-dependent quantum states and encoding new information about these systems. In particular, the time-time component of this tensor is related to the energy dispersion of the system. We applied this framework to a harmonic/inverted oscillator, a time-dependent harmonic oscillator, and a chain of generalized harmonic/inverted oscillators. We show some results on the scalar curvature associated with the time-dependent quantum geometric tensor and the generalized Berry curvature behavior on the transition from harmonic oscillators to inverted ones. Furthermore, we analyze the entanglement for the chain through purity analysis, obtaining that the purity for any excited state is zero in the mentioned transitions.