Quantum bifurcation diagrams

TL;DR

This paper introduces the concept of quantum bifurcation diagrams, illustrating how the asymptotic states of open quantum systems change qualitatively with parameter variations, and visualizes various bifurcations and chaos transitions.

Contribution

It defines quantum bifurcations and demonstrates their visualization using an N-boson open quantum dimer, including pitchfork, saddle-node, and period-doubling bifurcations.

Findings

Quantum bifurcations can be identified as changes in the asymptotic density matrix.

Visualization of quantum bifurcation diagrams for different types of bifurcations.

Identification of a purely quantum bifurcation of a novel nature.

Abstract

Asymptotic state of an open quantum system can undergo qualitative changes upon small variation of system parameters. We demonstrate it that such 'quantum bifurcations' can be appropriately defined and made visible as changes in the structure of the asymptotic density matrix. By using an $N$-boson open quantum dimer, we present quantum diagrams for the pitchfork and saddle-node bifurcations in the stationary case and visualize a period-doubling transition to chaos for the periodically modulated dimer. In the latter case, we also identify a specific bifurcation of purely quantum nature.