From GPE to KPZ: finite temperature dynamical structure factor of the 1D Bose gas

Manas Kulkarni and Austen Lamacraft 2013. Physical Review A

# Abstract

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.