Metriplectic Structure of a Radiation-Matter Interaction Toy Model

TL;DR

This paper introduces a simplified model of radiation-matter interaction using a metriplectic structure, combining Hamiltonian and dissipative dynamics to describe photon absorption by a two-level atom.

Contribution

It presents the first application of the metriplectic formalism to a radiation-matter interaction model, illustrating how dissipative processes can be incorporated into this framework.

Findings

The model reaches an asymptotically stable state with excited atomic levels populated.

The Hamiltonian describes free radiation, while the metric encodes radiation-matter coupling.

This approach paves the way for applying metriplectic formalism to nonlinear optics processes.

Abstract

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.