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We discuss the quantum--classical correspondence in a specific dissipativechaotic system, Duffing oscillator. We quantize it on the basis of quantumstate diffusion (QSD) which is a certain formulation for open quantum systemsand an effective tool for analyzing complex problems numerically. We consider asensitivity to initial conditions, `` pseudo-Lyapunov exponent '', andinvestigate it in detail, varying Planck constant effectively. We show that ina dissipative system there exists a certain critical stage in which thecrossover from classical to quantum behavior occurs. Furthermore, we show thatan effect of dissipation suppresses the occurrence of chaos in the quantumregion, while it, combined with the periodic external force, plays a crucialrole in the chaotic behaviors of classical system.Comment: 18 pages, 20 figure

Crossover from classical to quantum behavior of the Duffing oscillator through a pseudo-Lyapunov-exponent