Materassi Massimo, Marcucci Giulia, Conti Claudio
Institute for Complex Systems, National Research Council (ISC-CNR), Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy.
Institute for Space Astrophysics and Planetology (IAPS), National Institute of Astrophysics (INAF), 00133 Rome, Italy.
Entropy (Basel). 2022 Apr 4;24(4):506. doi: 10.3390/e24040506.
A dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines a Leibniz bracket; and a free energy, formed by a "Hamiltonian" and an entropy, playing the role of dynamics generator. Generally, these tensors are a Poisson bracket tensor, describing the Hamiltonian part of the dynamics, 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 is sufficient to describe 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, and the radiation has disappeared. First, a description of the system is used, based on the real-imaginary decomposition of the electromagnetic field phasor; then, the whole metriplectic system is re-written in terms of the phase-amplitude pair, named Madelung variables. This work is intended as a first result to pave the way for applying the metriplectic formalism to many other irreversible processes in nonlinear optics.
由度量辛结构定义的动力系统是一种耗散模型，其特征在于一对特定的张量，这对张量定义了一个李括号；以及一个自由能，它由一个“哈密顿量”和一个熵组成，起着动力学生成器的作用。通常，这些张量是一个泊松括号张量，用于描述动力学的哈密顿部分，以及一个对称度量张量，用于模拟纯耗散动力学。本文揭示了描述两能级原子简化双光子吸收的度量辛系统。哈密顿分量足以描述自由电磁辐射。度量分量编码了辐射与物质的耦合，驱使系统达到渐近稳定状态，在该状态下，原子的激发能级因吸收而被占据，且辐射消失。首先，基于电磁场相量的实虚部分解对系统进行描述；然后，用名为马德隆变量的相位 - 振幅对重新书写整个度量辛系统。这项工作旨在作为第一个成果，为将度量辛形式体系应用于非线性光学中的许多其他不可逆过程铺平道路。
