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 vertical bar x vertical bar < R. For a weakly interacting liquid there is parametrically wide regime n(-1) < R < xi (here n is the average density and xi 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.