Linear response of one-dimensional liquid ${}^4$He to external perturbations

We study the response of one-dimensional liquid ${}^4$He to weak perturbations relying on the dynamical structure factor, $S(q,\omega )$, recently obtained via ab-initio techniques [Phys. Rev. Lett. 116, 135302 (2016)]. We evaluate the drag force, $F_v$, experienced by an impurity moving along the system with velocity $v$ and the static response function, $\chi (q)$, describing the density modulations induced by a periodic perturbation with wave vector $q$.