Variational formulation of classical and quantum models for intense laser pulse propagation

TL;DR

This paper develops a unified variational framework for modeling intense laser pulse propagation in gases, deriving classical and quantum reduced models that preserve key physical properties and conserved quantities.

Contribution

It introduces a consistent variational approach to derive classical and quantum models for laser-gas interactions, ensuring conservation laws are maintained.

Findings

Derived reduced models preserving variational structure

Identified conserved quantities in the models

Established a parallel classical-quantum modeling framework

Abstract

We consider the theoretical description of intense laser pulses propagating through gases. Starting from a first-principles description of both the electromagnetic field and the electron motion within the gas atoms, we derive a hierarchy of reduced models. We obtain a parallel set of models, where the atomic electrons are treated classically on the one hand, and quantum-mechanically on the other. By working consistently in either a Lagrangian formulation or a Hamiltonian formulation, we ensure that our reduced models preserve the variational structure of the parent models. Taking advantage of the Hamiltonian formulation, we deduce a number of conserved quantities of the reduced models.