# Non-integrability of the semiclassical Jaynes--Cummings models without the rotating-wave approximation

## TL;DR

This paper investigates two semi-classical Jaynes--Cummings models without the rotating-wave approximation, demonstrating their non-integrability and analyzing their Hamiltonian structure for non-zero coupling.

## Contribution

It shows that both models are non-integrable and identifies the Hamiltonian structure of one model with a degenerated Poisson bracket.

## Key findings

- Both models are non-integrable.
- The Belobrov, Zaslavsky, and Tartakovsky model is Hamiltonian with a degenerated Poisson bracket.
- Non-zero coupling constant is essential for the Hamiltonian structure.

## Abstract

Two versions of the semi-classical Jaynes--Cummings model without the rotating wave approximation are investigated. It is shown that for a non-zero value of the coupling constant the version introduced by Belobrov, Zaslavsky, and Tartakovsky is Hamiltonian with respect to a certain degenerated Poisson bracket. Moreover, it is shown that both models are not integrable.