Metriplectic Structure of a Radiation-Matter Interaction Toy Model

A dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines the Leibniz brackets. Generally, these tensors are Poisson brackets tensor and a symmetric metric tensor that models purely dissipative dynamics. In this paper, the metriplectic system describing a simplified two-photon absorption by a two-level atom is disclosed. The Hamiltonian component describes the free electromagnetic radiation. The metric component encodes the radiation-matter coupling, driving the system to an asymptotically stable state in which the excited level of the atom is populated due to absorption. This work is intended as a first result to pave the way to apply the metriplectic formalism to many other irreversible processes in nonlinear optics.