The origin of the period-2T/7 quasi-breathing in disk-shaped Gross-Pitaevskii breathers

We address the origins of the quasi-periodic breathing observed in [Phys. Rev. X vol. 9, 021035 (2019)] in disk-shaped harmonically trapped two-dimensional Bose condensates, where the quasi-period Tquasi-breathing ~ 2T/7 and T is the period of the harmonic trap. We show that, due to an unexplained coincidence, the first instance of the collapse of the hydrodynamic description, at t∗ = arctan(√ 2)/(2π)T ~T/7, emerges as a 'skillful impostor' of the quasi-breathing half-period Tquasi-breathing/2. At the time t∗, the velocity field almost vanishes, supporting the requisite time-reversal invariance. We find that this phenomenon persists for scale-invariant gases in all spatial dimensions, being exact in one dimension and, likely, approximate in all others. In d dimensions, the quasi-breathing half-period assumes the form Tquasi-breathing/2 = t ∗ = arctan(√d)/(2π)T. Remaining unresolved is the origin of the period-2T breathing, reported in the same experiment.