Lee-Huang-Yang dynamics emergent from a direct Wigner representation

We demonstrate how the beyond-mean-field Lee-Huang-Yang (LHY) corrections and its related physics can be naturally incorporated into the representation of an ultracold Bose gas using the truncated Wigner approach without invoking effective energy terms or local density assumptions. By generating a Bogoliubov ground-state representation with appropriately tailored bare interaction strength $g_0$ and condensate density $n_0$, the expected initial energy and densities are obtained while retaining access to quantum effects beyond the reach of the extended Gross-Pitaevskii equation (EGPE) formulation. This approach enables the study of correlations, coherence decay, single realisations, and the onset of quantum fluctuation effects with growing interaction strength. Numerical demonstrations for a weakly interacting single-component Bose gas show that observables deviate significantly from both the plain GPE and the EGPE incorporating LHY corrections. In regimes of strong interaction, many of the interference effects predicted by the GPE and EGPE suppressed, and the EGPE offers no improvement over the plain GPE compared to the full Wigner model. In the weakly interaction limit, the EGPE appears accurate but resolving its deviation from mean-field results requires extensive ensemble averaging.