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

Abstract

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 $T_{\text{quasi-breathing}}\sim$~$2T/7$ 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 $t^{\ast }=\arctan (\sqrt{2})/(2\pi )T\approx T/7$, emerges as a `skillful impostor' of the quasi-breathing half-period $T_{\text{quasi-breathing}}/2$. At the time $t^{\ast }$, 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 $T_{\text{quasi-breathing}}/2\equiv t^{\ast }=\arctan (\sqrt{d})/(2\pi )T$. Remaining unresolved is the origin of the period-$2T$ breathing, reported in the same experiment.

15 pages, 3 figures. Submission to SciPost

References in corpus (3)

• Dynamical symmetry and breathers in a two-dimensional Bose gas
• Ideal-Gas Approach to Hydrodynamics
• Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves