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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Previous simulations of the one-dimensional Gross-Pitaevskii equation (GPE)with repulsive nonlinearity and a harmonic-oscillator trapping potential hinttowards the emergence of quasi-integrable dynamics -- in the sense ofquasi-periodic evolution of a moving dark soliton without any signs ofergodicity -- although this model does not belong to the list of integrableequations. To investigate this problem, we replace the full GPE by a suitablytruncated expansion over harmonic-oscillator eigenmodes (the Galerkinapproximation), which accurately reproduces the full dynamics, and then analyzethe system's dynamical spectrum. The analysis enables us to interpret theobserved quasi-integrability as the fact that the finite-mode dynamics alwaysproduces a quasi-discrete power spectrum, with no visible continuous component,the presence of the latter being a necessary manifestation of ergodicity. Thisconclusion remains true when a strong random-field component is added to theinitial conditions. On the other hand, the same analysis for the GPE in aninfinitely deep potential box leads to a clearly continuous power spectrum,typical for ergodic dynamics.

Probing quasi-integrability of the Gross-Pitaevskii equation in a harmonic-oscillator potential