Linear and integrable nonlinear evolution of the qutrit

TL;DR

This paper explores a nonlinear, integrable extension of the von Neumann equation for qutrits, revealing complex dynamics such as quasiperiodic motion, multiple equilibria, and limit cycles.

Contribution

It introduces a nonlinear, integrable generalization of the von Neumann equation for qutrits and analyzes its rich dynamical behavior.

Findings

Rich dynamics including quasiperiodic motion

Existence of multiple equilibria

Presence of limit cycles

Abstract

The nonlinear generalization of the von Neumann equation preserving convexity of the state space is studied in the nontrivial case of the qutrit. This equation can be cast into the integrable classical Riccati system of nonlinear ordinary differential equations. The solutions of such system are investigated in both the linear case corresponding to the standard von Neumann equation and the nonlinear one referring to the generalization of this equation. The analyzed dynamics of the qutrit is rich and includes quasiperiodic motion, multiple equilibria and limit cycles.