Signatures of Chaos in a Quasiperiodically Driven Quantum Impact Oscillator

Abstract: We demonstrate the emergence of quantum-chaotic dynamics in a quasiperiodically driven impact oscillator near the grazing condition. While previous studies of the quantum impact oscillator under periodic driving reported strange nonchaotic dynamics, we show that quasiperiodic driving produces robust signatures of chaos. The corresponding classical system undergoes a sharp grazing-induced transition from quasiperiodic motion to chaos, as established by bifurcation analysis, Lyapunov exponents, Fourier spectra, and the 0-1 test. In the quantum system, Shannon-entropy time series exhibit broadband spectra, 0-1 test values close to unity, and predominantly positive finite-time Lyapunov exponents for both rational and irrational driving-frequency ratios. Independent quantum diagnostics reinforce this result: the out-of-time-order correlator (OTOC) displays early-time exponential growth with nearly identical rates, while the golden-ratio drive leads to a substantially faster saturation of the OTOC. Fidelity exhibits an exponential decay regime that is approximately independent of perturbation strength. These results establish quasiperiodic driving near grazing as a mechanism for generating quantum-chaotic behavior and reveal that, although the initial onset of scrambling is largely insensitive to frequency-ratio rationality, the subsequent development of global scrambling is strongly influenced by the degree of irrationality of the drive.