# Bifurcation and chaos in nonlinear Lindblad equations

## TL;DR

This paper investigates nonlinear Lindblad equations in open quantum systems, revealing that they can exhibit bifurcations and chaos, which are relevant for certain experimental scenarios involving mean field theories or classical control.

## Contribution

It introduces the analysis of nonlinear Lindblad equations using classical dynamical systems techniques, highlighting the emergence of bifurcations and chaos in quantum dynamics.

## Key findings

- Nonlinear Lindblad equations can exhibit bifurcations.
- Chaotic dynamics are possible in these systems.
- Relevance to experimental quantum systems is discussed.

## Abstract

The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time evolution to be linear. However, when the density matrix is obtained from a mean field theory of interacting quantum systems or from a top-down control by a changing classical environment, the ensemble interpretation is inappropriate and nonlinear dynamics arise naturally. We therefore study the dynamical behavior of nonlinear Lindblad equations using the example of a two-level system. By using techniques developed for classical dynamical systems we show that various types of bifurcations and even chaotic dynamics can occur. We also discuss experimental situations for which our results could be relevant.