标题： Schrieffer-Wolff变换生成器的普适解 显示英文标题

标题： Universal solution to the Schrieffer-Wolff Transformation Generator

摘要： 施里弗-沃尔夫变换（SWT）是量子力学中一种重要的微扰方法，用于通过解耦低能和高能子空间来简化哈密顿量。现有的实现SWT的方法通常缺乏对任意微扰系统的通用适用性，或者无法提供SWT生成器的闭式解。本文提出了一种系统且统一的SWT框架，解决了这些不足之处。具体而言，我们推导出了一个适用于满足微扰处理条件的任意系统的SWT生成器的闭式解。此外，我们将该解扩展到具有周期性扰动的时间相关系统，涵盖所有频率范围。通过将其应用于分析与具有时间相关耦合的两能级系统耦合的非线性谐振器的色散位移，验证了此方法的有效性。 显示英文摘要

摘要： The Schrieffer-Wolff transformation (SWT) is an important perturbative method in quantum mechanics used to simplify Hamiltonians by decoupling low- and high-energy subspaces. Existing methods for implementing the SWT often lack general applicability to arbitrary perturbative systems or fail to provide a closed-form solution for the SWT generator. In this article, we present a systematic and unified framework for the SWT that addresses these shortcomings. Specifically, we derive a closed-form solution for the SWT generator that is universally applicable to any system that satisfies the conditions required for perturbative treatment. Furthermore, we extend this solution to time-dependent systems with periodic perturbations, covering all frequency regimes. The effectiveness of this approach is then demonstrated by applying it to analyze the dispersive shift of an anharmonic resonator coupled to a two-level system with time-dependent coupling.