English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Bose-Einstein condensates (BECs) confined in a two-dimensional (2D) harmonictrap are known to possess a hidden 2D Schr\"odinger symmetry, that is, theSchr\"odinger symmetry modified by a trapping potential. Spontaneous breakingof this symmetry gives rise to a breathing motion of the BEC, whose oscillationfrequency is robustly determined by the strength of the harmonic trap. In thispaper, we demonstrate that the concept of the 2D Schr\"odinger symmetry can beapplied to predict the nature of three dimensional (3D) collective modespropagating along a condensate confined in an elongated trap. We find threekinds of collective modes whose existence is robustly ensured by theSchr\"odinger symmetry, which are physically interpreted as one breather modeand two Kelvin-ripple complex modes, i.e., composite modes in which the vortexcore and the condensate surface oscillate interactively. We provide analyticalexpressions for the dispersion relations (energy-momentum relation) of thesemodes using the Bogoliubov theory [D. A. Takahashi and M. Nitta, Ann. Phys.354, 101 (2015)]. Furthermore, we point out that these modes can be interpretedas "quasi-massive-Nambu-Goldstone (NG) modes", that is, they have theproperties of both quasi-NG and massive NG modes: quasi-NG modes appear when asymmetry of a part of a Lagrangian, which is not a symmetry of full aLagrangian, is spontaneously broken, while massive NG modes appear when amodified symmetry is spontaneously broken.

Two-dimensional Schr\"odinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes