As experimental probes have matured to observe ultrafast transient and high frequency responses of materials and devices, so to have the theoretical methods to numerically and analytically simulate time- and frequency-resolved transport. In this review article, we discuss recent progress in the development of the time-dependent and frequency-dependent non-equilibrium Green function (NEGF) technique. We begin with an overview of the theoretical underpinnings of the underlying Kadanoff-Baym equations and derive the fundamental NEGF equations in the time and frequency domains. We discuss how these methods have been applied to a variety of condensed matter systems such as molecular electronics, nanoscale transistors, and superconductors. In addition, we survey the application of NEGF in fields beyond condensed matter, where it has been used to study thermalization in ultra-cold atoms and to understand leptogenesis in the early universe. Throughout, we pay special attention to the challenges of incorporating contacts and interactions, as the NEGF method is uniquely capable of accounting for such features.

中文翻译：

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用非平衡格林函数模拟相互作用的瞬态现象的综述

随着实验探针在观察材料和器件的超快瞬态和高频响应方面已经成熟，因此具有数值和解析模拟时间和频率分辨输运的理论方法。在这篇评论文章中，我们讨论了时间相关和频率相关的非平衡格林函数 (NEGF) 技术的最新进展。我们首先概述基础 Kadanoff-Baym 方程的理论基础，并推导出时域和频域中的基本 NEGF 方程。我们讨论了这些方法如何应用于各种凝聚态系统，如分子电子学、纳米级晶体管和超导体。此外，我们考察了NEGF在凝聚态以外领域的应用，它已被用于研究超冷原子的热化和了解早期宇宙的轻质发生。在整个过程中，我们特别关注结合接触和交互的挑战，因为 NEGF 方法独特地能够解释这些特征。