用于非平衡关联函数的广义凯尔迪什形式及其在涨落动力学中的应用
Generalized Keldysh formalism for nonequilibrium correlation functions and its application to fluctuation dynamics
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中文总结 AI 辅助
针对计算关联量子材料非平衡两粒子关联函数的挑战，提出基于广义凯尔迪什形式的方法，引入线性积分方程及无矩阵求解器，结合非平衡动态平均场理论，揭示序参量涨落动力学特性，为评估非平衡关联函数提供实用途径。
中文摘要 AI 辅助
时间分辨光谱学的最新进展使人们越来越容易研究关联量子材料中的集体动力学。然而，计算相应的非平衡两粒子关联函数仍然是一个重大挑战。在此，通过在广义凯尔迪什形式中引入依赖于轮廓的虚拟探测场，我们提出了一种计算此类关联函数的方法，该方法包含描述集体动力学所必需的顶点修正。特别是，我们引入了一个线性积分方程来计算关联函数，而无需明确构建四时间顶点核，并基于量子张量列开发了其无矩阵克雷洛夫求解器。将我们的方法与非平衡动态平均场理论相结合，我们表明非平衡对称破缺态中序参量的涨落动力学显著取决于是否包含顶点修正，并且涨落及其衰减时间在非热临界点附近增长。因此，我们的方法为评估非平衡关联函数提供了一条实用途径，这些函数正成为表征远离平衡态的关键可观测量。
英文摘要
Recent advances in time-resolved spectroscopies provide increasing access to collective dynamics in correlated quantum materials. However, computing the corresponding nonequilibrium two-particle correlation functions remains a major challenge. Here, by introducing a contour-dependent virtual probe field within the generalized Keldysh formalism, we propose an approach that computes such correlation functions with the vertex corrections essential for describing collective dynamics. In particular, we introduce a linear integral equation that computes the correlation functions without explicitly constructing the four-time vertex kernel, and develop its matrix-free Krylov solver based on quantics tensor trains. Combining our method with nonequilibrium dynamical mean-field theory, we show that the fluctuation dynamics of the order parameter in a nonequilibrium symmetry-broken state depends significantly on whether vertex corrections are included, and that the fluctuation and its decay time grow near the nonthermal critical point. Our approach thus provides a practical route for evaluating nonequilibrium correlation functions, which are emerging as key observables for characterizing states far from equilibrium.
