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

TL;DR

This paper explores how chaos and the quantum-classical transition in rf-SQUID systems depend on environmental coupling, revealing non-monotonic chaos behavior and a universal scaling law related to quantum uncertainty.

Contribution

It demonstrates the non-monotonic dependence of chaos on coupling strength and establishes a universal scaling law in rf-SQUID systems with varying effective Planck's constant.

Findings

Chaos emerges with non-monotonic dependence on coupling strength D.

Quantum and classical dynamics proximity scales with chaos measure.

Scaling law holds for smaller effective Planck's constant, indicating universality.

Abstract

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.