Breakdown of homoclinic orbits to L1 of the hydrogen atom in a circularly polarized microwave field

Amadeu Delshams, Mercè Ollé, Juan Ramon Pacha, Óscar Rodríguez

incompletemedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper establishes the asymptotic laws and exponents numerically and via semi-analytical reductions (normal form + a Toy CP model + a numerically evaluated Melnikov integral), but it does not furnish a full rigorous proof for the exact CP Hamiltonian; it explicitly notes the lack of directly applicable theory and computes key inner data numerically. The model’s solution correctly reproduces the exponents, exponential factor, and the synodic–resonant link, and outlines a plausible inner-equation mechanism, but it does not provide a complete, assumption-checked derivation (e.g., the μ=28/9 singular order is asserted without a full calculation and hypotheses verification). Hence both are consistent but not fully proved.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The manuscript compellingly identifies nontrivial exponents (29/18 and 19/9), isolates the amended-pendulum mechanism, and provides careful numerical and semi-analytical corroboration, including a Toy CP model and numerically evaluated Melnikov integrals. However, a rigorous derivation for the exact CP Hamiltonian is not provided (and is explicitly deferred). Clarifying this scope, fixing a minor coefficient-relation typo, and better delineating what is proved for Toy CP vs. conjectured for CP would significantly enhance the paper’s clarity and impact.