论文标题
扰动性非线性量子传输的理论II：希尔伯特空间截断，规格不变性和二阶传输在空间均匀的，时变的电场中
Theory of perturbatively nonlinear quantum transport II: Hilbert space truncation, gauge invariance, and second order transport in a spatially uniform, time-varying electric field
论文作者
论文摘要
本文是三部曲的第二篇，该三部曲涉及一般量子系统的扰动响应，可能是非平凡的基态几何形状，超出了线性秩序。在这里，我们建立了简洁的一般公式，用于对速度量规上的空间均匀，时变的电场的二阶响应，这些电场是$ \ textit {明显的} $，没有静态极限偏差差异。我们首先讨论弯曲空间中的一般量子演变，然后详细介绍这种情况如何是希尔伯特空间截断的自然副产品，并指出与所得有限曲线相关的关键微妙之处。然后，我们介绍了经常用于量子传输理论的两个流行仪表，即速度量规和长度仪表，并讨论它们如何考虑截断引起的曲率效应，尽管截短，但它们如何考虑截断引起的曲率效应。我们重点介绍了文献中细微的形式差异。最后，我们提供了一个通用方案，用于删除速度量规$ \ textit {没有} $频率扩展中的静态限制虚假差异，并呈现简洁且全面的绿色功能公式，以响应最多二阶。作为我们理论的特定方面的应用，在第I和III部分中分析了选定病例中的二阶费用当前响应。
This article is the second of a trilogy that addresses the perturbative response of general quantum systems, with possibly nontrivial ground state geometry, beyond linear order. Here, we establish concise, general formulae for second order response to a spatially uniform, time-varying electric field in the velocity gauge that are $\textit{manifestly}$ free of static limit spurious divergences. We first discuss general quantum evolution in a curved space, then detail how such a situation is a natural byproduct of Hilbert space truncation, and point out crucial subtleties associated with the resulting finite curvatures. We then present a geometric perspective of the two popular gauges often used in quantum transport theories, the velocity gauge and the length gauge, and discuss how they, taking truncation-induced curvature effects into account, naturally lead to the same results in spite of the truncation. We highlight subtle formal discrepancies in the literature. Finally, we provide a general scheme for removing static limit spurious divergences in the velocity gauge $\textit{without}$ frequency expansions and present concise and comprehensive Green's function formulae for responses up to second order. As an application of specific aspects of our theory, second order charge current responses in selected cases are analyzed in parts I and III.
