Scaling Behavior in Noisy Dicke Model Simulations

We report the discovery of a universal scaling law governing information fragmentation in open quantum systems modeled by the Dicke Hamiltonian. Through systematic numerical simulations using the Lindblad master equation formalism on a single NVIDIA A100 GPU (80GB PCIe) via Lambda GPU Cloud services, we identify a discontinuous phase transition in the scaling exponent α for system sizes up to N=50. We demonstrate that as dephasing noise increases, the system transitions from a coherent phase (α ≈ -0.05) to a fragmented phase characterized by the '-1.36 Functional Collapse Law'. This discovery provides a precise quantitative signature for phase transitions in collective quantum systems, with significant implications for quantum error correction, decoherence protection in quantum devices, and the study of quantum-classical boundaries. Repository includes: Manuscript (PDF): Full theoretical framework and analysis. nature_results.csv: Primary data for the -1.36 scaling phase. HealthyLow-Noise.csv: Control data for the coherent phase. run_physics.py: Consolidated QuTiP simulation script for reproducibility.