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

Jordi Torrents, Vanja Dunjko, Marina Gonchenko, Gregory E. Astrakharchik, Maxim Olshanii

SciPost Phys. 12, 092 (2022) · published 14 March 2022

- doi: 10.21468/SciPostPhys.12.3.092
- Submissions/Reports

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

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Jordi Torrents, -
^{2}Vanja Dunjko, -
^{1}Marina Gonchenko, -
^{3}Grigori E. Astrakharchik, -
^{2}Maxim Olshanii

^{1}Universitat de Barcelona / University of Barcelona [UB]^{2}University of Massachusetts Boston^{3}Universitat Politècnica de Catalunya [UPC]

- Generalitat de Catalunya / Government of Catalonia
- Ministerio de Ciencia e Innovación
- Ministerio de Economía y Competitividad (MINECO) (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])
- National Science Foundation [NSF]
- United States - Israel Binational Science Foundation (through Organization: United States-Israel Binational Science Foundation [BSF])