Knizhnik-Zamolodchikov方程的量子非平衡动力学
Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations
摘要：
我们考虑一组非定常量子模型。我们表明，可以使用与共形场论中关联函数的Knizhnik-Zamolodchikov（KZ）方程的联系来研究它们的动力学。我们特别考虑边界Wess-Zumino-Novikov-Witten模型，其中初级场的微分方程由KZ方程的扩展定义，并探索与动力系统的联系。作为所提出的方法的可操作性的一个例子，我们提供了一个精确的解决方案的动力系统，这是一个特定的多级推广的两级朗道-Zenner系统在文献中称为Demkov-Osherov模型。该方法可用于研究各种多能级系统中的非平衡动力学，从相应的KZ方程的解。
英文摘要：
We consider a set of non-stationary quantum models. We show that their dynamics can be studied using links to Knizhnik-Zamolodchikov (KZ) equations for correlation functions in conformal field theories. We specifically consider the boundary Wess-Zumino-Novikov-Witten model, where equations for correlators of primary fields are defined by an extension of KZ equations and explore the links to dynamical systems. As an example of the workability of the proposed method, we provide an exact solution to a dynamical system that is a specific multi-level generalization of the two-level Landau-Zenner system known in the literature as the Demkov-Osherov model. The method can be used to study the nonequilibrium dynamics in various multi-level systems from the solution of the corresponding KZ equations.
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