  We investigate universal properties of one-dimensional multi-component
systems comprised of fermions, bosons, or an arbitrary mixture, with contact
interactions and subjected to an external potential. The masses and the
coupling strengths between different types of particles are allowed to be
different and we also take into account the presence of an arbitrary magnetic
field. We show that the momentum distribution of these systems exhibits a
universal $n_\sigma(k) \sim C_\sigma/k^4$ decay with $C_\sigma$ the contact of
species $\sigma$ which can be computed from the derivatives of an appropriate
thermodynamic potential with respect to the scattering lengths. In the case of
integrable fermionic systems we argue that at fixed density and repulsive
interactions the total contact reaches its maximum in the balanced system and
monotonically decreases to zero as we increase the magnetic field. The converse
effect is present in integrable bosonic systems: the contact is largest in the
fully polarized state and reaches its minimum when all states are equally
populated. We obtain short distance expansions for the Green's function and
pair distribution function and show that the coefficients of these expansions
can be expressed in terms of the density, kinetic energy and contact. In
addition we derive universal thermodynamic identities relating the total energy
of the system, pressure, trapping energy and contact. Our results are valid at
zero and finite temperature, for homogeneous or trapped systems and for
few-body or many-body states.
