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We consider a gas of repulsive $N$-component fermions confined in aring-shaped potential, subject to an effective magnetic field. For largerepulsion strengths, we work out a Bethe ansatz scheme to compute the two-pointcorrelation matrix and then the one-particle density matrix. Our results holdsin the mesoscopic regime of finite but sufficiently large number of particlesand system size that are not accessible by numerics. We access the momentumdistribution of the system and analyse its specific dependence of interaction,magnetic field and number of components $N$. In the context of cold atoms, theexact computation of the correlation matrix to determine the interferencepatterns that are produced by releasing cold atoms from ring traps is carriedout.

Exact one-particle density matrix for SU($N$) fermionic matter-waves in the strong repulsive limit