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 $\propto \mathrm{\mid }k{\mathrm{\mid }}^{3\mathrm{/}2}$ 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.