Effective Open Quantum Dynamics with Z₃ Symmetry: Spectral Confinement, Fibonacci Recurrence, and a Falsifiable Prediction

Key Points

• The aim is to develop a theoretical framework for understanding open quantum dynamics with Z₃ symmetry.
• Developed an effective field theory framework for open quantum systems.
• Analyzed the dynamics in a 2D invariant subspace facilitated by spectral confinement.
• Defined an infrared closure class to establish recurrence structures and identify a fixed point.
• Demonstrated a second-order recurrence structure leading to Fibonacci form.
• Identified the golden ratio as a fixed point in recursive relationships.
• Proposed a falsifiable prediction distinguishing between algebraic and exponential decay behaviors under sub-ohmic conditions.