  One-dimensional world is very unusual as there is an interplay between
quantum statistics and geometry, and a strong short-range repulsion between
atoms mimics Fermi exclusion principle, fermionizing the system. Instead, a
system with a large number of components with a single atom in each, on the
opposite acquires many bosonic properties. We study the ground-state properties
a multi-component Fermi gas trapped in a harmonic trap by fixed-node diffusion
Monte Carlo method. We investigate how the energetic properties (energy,
contact) and correlation functions (density profile and momentum distribution)
evolve as the number of components is changed. It is shown that the system
fermionizes in the limit of strong interactions. Analytical expression are
derived in the limit of weak interactions within the local density
approximation for arbitrary number of components and for one plus one particle
using an exact solution.
