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

TL;DR

This paper investigates the finite temperature dynamical structure factor of a 1D Bose gas, revealing anomalous phonon peak broadening linked to three-phonon interactions and KPZ universality.

Contribution

It introduces a numerical study connecting phonon peak broadening in a 1D Bose gas to KPZ universality through resonant three-phonon interactions.

Findings

Phonon peak width scales as |k|^{3/2} at low wavevectors

Resonant three-phonon interactions cause anomalous broadening

Connection established between Bose gas dynamics and KPZ universality

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.