  We investigate how the different velocities characterizing the low-energy
spectral properties and the low-temperature thermodynamics of one-dimensional
correlated electron systems (Luttinger liquids) affect the transport properties
of ring-like conductors. The Luttinger liquid ring is coupled to two
noninteracting leads and pierced by a magnetic flux. We study the flux
dependence of the linear conductance. It shows a dip structure which is
governed by the interaction dependent velocities. Our work extends an earlier
study which was restricted to rather specific choices of the interaction
parameters. We show that for generic repulsive two-particle interactions the
number of dips can be estimated from the ratio of the charge current velocity
and the spin velocity. In addition, we clarify the range of validity of the
central approximation underlying the earlier study.
