Emptiness Formation Probability in 1D Bose Liquids

We study emptiness formation probability (EFP) in interacting 1D Bose liquids. That is the probability that a snapshot of its ground state reveals exactly zero number of particles within the interval $|x|<R$. For a weakly interacting liquid there is parametrically wide regime $n^{-1} < R <ξ$ (here $n$ is the average density and $ξ$ is the healing length), where EFP exhibits a non-trivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [A. Abanov, 2004] to study quantitative details of these regime and compare it with previously reported limited cases.

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