Lyapunov Dynamics in Entangled Biphoton Spectroscopy

We develop a Lyapunov-based framework to model the evolution of entangled biphotons interacting with cavity and material modes. Using Gaussian-preserving dynamics and M{\o}ller operators, we map input joint spectral amplitudes to experimentally measurable joint spectral intensities. Our model reproduces key features of observed spectra and reveals off-diagonal correlations arising from cavity decay, providing a scalable and tractable tool for quantum spectroscopic analysis.