Parameter Scaling in the Decoherent Quantum-Classical Transition for chaotic rf-SQUIDs

We numerically investigated the quantum-classical transition in rf-SQUID systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent $\lambda_{m}$, exhibits non-monotonic behavior as a function of the coupling strength $D$. By measuring the proximity of quantum and classical evolution with the uncertainty of dynamics, we show that the uncertainty is a monotonic function of $\lambda _{m}/D$. In addition, the scaling holds in SQUID systems to a relatively smaller $\hbar_{eff}$, suggesting the universality for this scaling.