Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations

TL;DR

This paper introduces a novel approach to study non-stationary quantum models by linking their dynamics to Knizhnik-Zamolodchikov equations from conformal field theory, providing exact solutions for complex multi-level systems.

Contribution

It establishes a connection between quantum nonequilibrium dynamics and KZ equations, enabling exact solutions for multi-level quantum systems like the Demkov-Osherov model.

Findings

Exact solution for a multi-level generalization of the Landau-Zener system.

Method applies to various multi-level quantum systems.

Demonstrates the utility of KZ equations in quantum dynamics.

Abstract

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.