Thermodynamics and Transport Theory of Nonlinear Multimoded Photonic Circuits

Nonlinear multimode photonic circuits provide a platform that bridge optics, statistical physics, and many-body transport. In this seminar, I will show how Kerr nonlinearities and intermodal coupling drive energy redistribution across optical modes, leading to Rayleigh–Jeans–type equilibrium distributions governed by conserved power and Hamiltonian energy. We develop a kinetic and scaling framework for relaxation in mode space, identifying how connectivity, disorder, and spectral structure control thermalization rates and thermal states. I will further discuss mappings of multimode dynamics to interacting spin models, revealing optical analogs of collective phases and symmetry-breaking transitions, as well as the emergence of nonconventional thermal states in few-mode (both classical and quantum) bosonic systems. These results position multimode photonics as a controllable testbed for conservative wave thermalization, mode transport, and many-body phenomena.