Quantum fluctuations and chaos in fully connected spin models

We investigate beyond-mean-field dynamics in a fully connected $\mathrm{SU}(3)$ spin-exchange model, focusing on the interplay between chaotic dynamics and quantum fluctuations. Using the two-particle irreducible (2PI) effective action formalism, we derive equations of motion that systematically account for higher-order correlations generated by interactions, and demonstrate how quantum fluctuations can regularize chaotic dynamics displayed by macroscopic observables. Our results show that an accurate treatment of fluctuations is essential for describing macroscopic dynamics in quantum many-body systems and promote 2PI as a robust framework for connecting microscopic correlations to macroscopic nonequilibrium phenomena.