From GPE to KPZ: finite temperature dynamical structure factor of the 1D   Bose gas
  We study the finite temperature dynamical structure factor $S(k,\omega)$ of a 1D Bose gas using numerical simulations of the Gross--Pitaevskii equation appropriate to a weakly interacting system. The lineshape of the phonon peaks in $S(k,\omega)$ has a width $\propto |k|^{3/2}$ at low wavevectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar--Parisi--Zhang universality class of dynamical critical phenomena. 
Manas Kulkarni and Austen Lamacraft
cond-mat.quant-gas