Dynamics of Quantum Analogs of Classical Impact Oscillators

Abstract: This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum systems, governed by linear equations, appear to forbid such dynamics. Through simulations of unforced, forced, and dissipative quantum oscillators, we uncover quasiperiodicity, strange nonchaotic dynamics, and even chaos in the presence of dissipation. Using entropy time series, Fourier spectra, OTOCs, Lyapunov analysis, and the 0-1 test, we demonstrate that quantum systems can exhibit rich dynamical signatures analogous to classical nonlinear systems, bridging quantum mechanics and chaos theory.