Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes

TL;DR

This paper investigates how chaos emerges in a coupled classical-quantum system modeled by a semiquantum Hamiltonian, especially near quantum critical points that separate stable and unstable regimes.

Contribution

It introduces a nonlinear model based on a semiquantum Hamiltonian with a bosonic BCS-like structure, highlighting the influence of quantum regimes on classical chaos.

Findings

Chaos arises near quantum critical points.

Quantum subsystem strongly influences classical dynamics.

Stable and unstable regimes are separated by quantum criticality.

Abstract

We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.