Quantum chaos in quantum dots coupled to bosons

TL;DR

This paper investigates quantum chaos in quantum dots coupled to bosons by analyzing a modified Dicke Hamiltonian, revealing transitions from integrable to chaotic dynamics through bifurcation analysis and quantum corrections.

Contribution

It introduces a quantum-corrected logistic map derived from a Dicke Hamiltonian coupled to a harmonic oscillator bath, exploring chaos transitions in this quantum system.

Findings

Transition from integrable to chaotic and hyperchaotic regimes as control parameter increases

Lyapunov exponents indicate chaos onset in the model

Bifurcation diagrams illustrate the dynamical behavior changes

Abstract

Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum corrections. Some basic dynamical properties, such as Lyapunov exponents and bifurcation diagram of the model are studied. we show that in this model, the transition from integrable motion to periodic, chaotic and hyperchaotic as the control parameter $r$ is increased.