Minimum number of drive frequencies needed for chaos in the kicked rotor

Determine the minimal number of distinct harmonic components in the time-periodic drive of the kicked rotor Hamiltonian H(t)=L^2/(2I)+K cos(θ) Σ_{n∈ℤ} δ(t−nT) that are sufficient to produce classical chaotic dynamics, and characterize how the onset of chaos depends on the number and amplitudes of these frequency components.

Background

In the comparison between the high-harmonic-generation simple-man model and the kicked rotor, the authors emphasize that a train of pulses can be represented as an infinite sum over harmonic frequencies (plus a DC component). They note that understanding the transition from single-frequency driving to multi-frequency excitation in producing chaos is incomplete.

They explicitly pose the question of how many frequencies are required to observe chaos, indicating a concrete unresolved aspect of the kicked-rotor dynamics under multi-harmonic drives.

References

This raises several additional questions: 1) How many frequencies are necessary to begin to observe chaos in the kicked rotor?

— Attochaos I: The classically chaotic postcursor of high harmonic generation (2405.05804 - Berkheim et al., 9 May 2024) in Section “Future Work”, Subsection “From simple-man to kicked rotor”