Universal high frequency high momentum behavior of dynamic structure factor in one dimensional interacting boson gas

We study the short-distance and short-time structure of density-density correlation in one dimensional repulsively interacting boson gas. A compact universal formula is obtained for the high frequency high momentum asymptotic behavior of dynamic structure factor. We observe non-monotonous behavior in the dependence of DSF on interacting strength and qualitative change in the singular behavior in different region of $q^2/\omega$. Possible experimental applications are discussed.