标题： 特征算符方法在施里弗-沃尔夫微扰理论和色散相互作用中的应用 显示英文标题

标题： Eigenoperator approach to Schrieffer-Wolff perturbation theory and dispersive interactions

摘要： 现代量子物理非常模块化：我们首先理解基本构建块（“XXZ哈密顿量”、“Jaynes-Cummings”等），然后将它们组合起来以探索新的效应。一个典型的例子是将已知系统放置在光学腔中。Schrieffer-Wolff微扰方法特别适合处理这些问题，因为它将微扰展开表示为对哈密顿量的操作符修正，这比传统非简并微扰理论中的能级修正更直观。然而，该方法缺乏系统的方法，并且很大程度上仍是一个小众话题。在这些笔记中，我们讨论如何利用\emph{本征算子分解}，一个在开放量子系统中广泛使用的概念，来构建Schrieffer-Wolff微扰理论的直观且系统化的表述。为了说明这一点，我们重新审视文献中各种新旧论文，并展示如何使用本征操作符来解决它们。特别强调的是那些耦合两个具有非常不同跃迁频率的系统的微扰（高度非共振），导致所谓的色散相互作用。 显示英文摘要

摘要： Modern quantum physics is very modular: we first understand basic building blocks (``XXZ Hamiltonian'' ``Jaynes-Cummings'' etc.) and then combine them to explore novel effects. A typical example is placing known systems inside an optical cavity. The Schrieffer-Wolff perturbation method is particularly suited for dealing with these problems, since it casts the perturbation expansion in terms of operator corrections to a Hamiltonian, which is more intuitive than energy level corrections, as in traditional time-independent perturbation theory. However, the method lacks a systematic approach.% and has largely remained a niche topic. In these notes we discuss how \emph{eigenoperator decompositions}, a concept largely used in open quantum systems, can be employed to construct an intuitive and systematic formulation of Schrieffer-Wolff perturbation theory. To illustrate this we revisit various papers in the literature, old and new, and show how they can instead be solved using eigenoperators. Particular emphasis is given to perturbations that couple two systems with very different transition frequencies (highly off-resonance), leading to the so-called dispersive interactions.