  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.
