On the Generalized Maxwell-Bloch Equations

TL;DR

This paper introduces a Hamiltonian framework for the Maxwell-Bloch equations, generalizing them via Lie group parameters, and explores new symmetries and conserved quantities within this broader mathematical structure.

Contribution

It presents a novel Hamiltonian formulation of the Maxwell-Bloch equations as part of a family parameterized by Lie groups, extending their mathematical understanding.

Findings

New Hamiltonian structure for Maxwell-Bloch equations

Generalization to a family parameterized by Lie groups

Identification of new symmetries and conserved quantities

Abstract

A new Hamiltonian structure of the Maxwell-Bloch equations is described. In this setting the Maxwell-Bloch equations appear as a member of a family of generalized Maxwell-Bloch systems. The family is parameterized by compact semi-simple Lie groups, the original Maxwell-Bloch system being the member corresponding to SU(2). The Hamiltonian structure is then used in the construction of a new family of symmetries and the associated conserved quantities of the Maxwell-Bloch equations.