Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations

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 WessZumino-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.

Automated summary

In this study, a set of non-stationary quantum models are considered. It is shown that their dynamics can be studied by linking them to Knizhnik-Zamolodchikov (KZ) equations for correlation functions in conformal field theories. The boundary Wess-Zumino-Novikov-Witten model is specifically explored, where equations for correlators of primary fields are defined by an extension of KZ equations, revealing the connections to dynamical systems. As an example, an exact solution to a dynamical system that is a specific multi-level generalization of the two-level Landau-Zenner system, known as the Demkov-Osherov model, is provided to demonstrate the feasibility of the proposed method. The method can be used to study the nonequilibrium dynamics in various multi-level systems from the solution of the corresponding KZ equations.