Dynamics of excitations in a one-dimensional Bose liquid

We studied the dynamical structure factor $S(q,\omega)$ of interacting bosons in one-dimension. The sharp resonant peak $S(q,\omega) \propto \delta(\omega - \epsilon(q))$ as predicted by the Bogolubov theory is transformed into a power law singularity, $S(q,\omega) \propto (\omega - \epsilon(q))^{-\mu(q)}$ due to the strong quantum fluctuations. The corresponding momentum dependent exponent $\mu(q)$ is evaluated using the Lieb-Liniger model. The full momentum dependence $\mu(q)$ has been found in the strongly interaction regime using the Fermi Bose mapping. For the large momentum $q$ the different method allows us to express the exponent through the Luttinger liquid parameters. The two results agree in their common region of applicability.