Crossover from Classical to Quantum Behavior in Duffing Oscillator through “Pseudo-Lyapunov Exponent”

Abstract

We discuss the quantum–classical correspondence in a specific dissipative chaotic system, Duffing oscillator. We quantize it on the basis of quantum state diffusion (QSD) that is a certain formulation for quantum open systems and a useful tool for analyzing nonlinear problems and their classical limit. We define a “pseudo-Lyapunov exponent” and investigate the behavior of this quantity varying Planck constant effectively. We show that in a dissipative system there exists some critical stage in which the crossover from classical to quantum behavior occurs. Furthermore, we show that the role of dissipation changes for quantized Duffing oscillator since the effect of dissipation is important for the occurrence of chaos in classical mechanics but suppresses it in quantum region.