  We study the three-fermion problem within a 1D model of a Feshbach resonance
in order to gain insight into how the FFLO-like state at small negative
scattering lengths evolves into a Bose-Fermi mixture at small positive
scattering lengths. The FFLO state possesses an oscillating superfluid
correlation function, while in a Bose-Fermi mixture correlations are monotonic.
We find that this behavior is is already present at the 3-body level. We
present an exact study of the 3-body problem, and gain extra insights by
considering worldlines of a path integral Monte-Carlo calculation.
