Dynamical Chaos in a Dissipative Driven Quantum Soft Impact Oscillator

TL;DR

This paper explores how quantum dissipative systems exhibit chaos through a driven soft impact oscillator, revealing complex transitions from periodic to chaotic behavior influenced by environmental noise.

Contribution

It introduces a quantum Langevin equation approach to analyze impact-induced chaos and demonstrates the persistence of chaos under quantum dissipation.

Findings

Chaos persists in quantum dissipative impact oscillators.

Dynamical transitions include bifurcations and chaos.

Environmental fluctuations significantly influence quantum non-linear dynamics.

Abstract

Dynamical chaos in a periodically driven, dissipative soft impact oscillator is investigated in the quantum regime using the complex-number quantum Langevin equation (c-number QLE). The averaged system dynamics are analyzed through a comprehensive suite of time-series diagnostics, including bifurcation diagrams, Lyapunov exponents, Fourier spectra, and the 0-1 test. Systematic variation of the wall position reveals a rich sequence of dynamical transitions and grazing bifurcations, progressing from periodic to multiperiodic motion and culminating in chaotic behavior. These results demonstrate the persistence of impact-induced chaos under quantum dissipation and elucidate how environmental fluctuations influence non-linear dynamics in open quantum systems.