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 $q$.
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