参数空间的量子几何：弯曲系统的一个提议
Quantum geometry of the parameter space: a proposal for curved systems
AI总结：
本文提出将量子几何张量推广至参数依赖的弯曲空间高维情形，引入等价定义，并通过二维示例比较广义与传统张量，揭示量子度量张量和Berry曲率的独特几何性质，同时探讨解析与微扰方法的差异。
摘要：
在本文中，我们将参数依赖的弯曲空间的量子几何张量扩展到更高维度，并引入一个等价定义，该定义推广了Zanardi等人的张量表述。参数依赖的度量以纯几何方式修改了量子度量张量和Berry曲率的行为。我们重点关注理解使用广义张量与传统张量时在高维度中出现的差异。通过比较分析，并以二维示例进行说明，我们强调了量子度量张量和Berry曲率的独特量子几何性质。此外，我们探讨了在解决问题时解析方法与微扰方法之间的差异。
英文摘要：
In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent metric modifies the behavior of both the quantum metric tensor and Berry curvature in a purely geometric way. Our focus is on understanding the distinctions in higher dimensions that emerge when using the generalized tensor compared to the conventional one. Through a comparative analysis, illustrated with examples in two dimensions, we highlight unique quantum geometric properties for both the quantum metric tensor and the Berry curvature. Additionally, we explore differences between analytical and perturbative approaches in solving the problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
