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An autoresonant approach for exciting spacetime quasicrystals in Bose-Einstein condensates is proposed by employing two-component chirped frequency parametric driving or modulation of the interaction strength within Gross-Pitaevskii equation. A weakly nonlinear theory of the process is developed using Whitham's averaged variational principle yielding reduction to a two-degrees-of-freedom dynamical system in action-angle variables. Additionally, the theory also delineates permissible driving parameters and establishes thresholds on the driving amplitudes required for autoresonant excitation.
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Frièdland et al. (2024) studied this question.
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