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Necessary conditions for strong chaotic recollisions in the 1D soft-Coulomb HHG model

Determine whether either inequality between the rescaled field amplitude and Coulomb parameter—namely, \tilde{E}_{0}≤\tilde{C} or \tilde{E}_{0}≥\tilde{C}—is necessary for the existence of strong chaotic recollisions in the one-dimensional soft-Coulomb Hamiltonian H(x,p,t)=p^2/(2m)−qxE_{0} sin(ω t)−C/√(x^2+a), and characterize the parametric regimes (in terms of \tilde{E}_{0}, \tilde{C}, and ionization time) that yield such trajectories.

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Background

Combining recollision energy thresholds and Lyapunov-based chaos diagnostics, the authors identify regions with strong chaotic recollisions but note a lack of clarity regarding the necessary relations between the rescaled field amplitude and the Coulomb parameter.

They explicitly state their inability to assert which inequality is required, indicating an open characterization problem in the parametric landscape of the HHG classical model.

References

We cannot say that \tilde{E}{0}\leq \tilde{C} or \tilde{E}{0}\geq \tilde{C} are necessarily demanded for strong chaotic recollisions; both relations might work.

— Attochaos I: The classically chaotic postcursor of high harmonic generation (2405.05804 - Berkheim et al., 9 May 2024) in Section “Attochaos and strong chaotic recollisions”