Emptiness formation probability in one-dimensional Bose liquids

We study the emptiness formation probability (EFP) in interacting one-dimensional Bose liquids, which is the probability that a snapshot of its ground state reveals exactly zero particles within the interval |x|<R. For a weakly interacting liquid there is parametrically wide regime n-1<R<ζ (here n is the average density and ζ is the healing length) where EFP exhibits a nontrivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [NATO Science Series II: Mathematics, Physics and Chemistry (2004), Vol. 221] to study quantitative details of these regime and compare it with previously reported special cases.