  The presence of spin-orbit coupling affects the spontaneously flowing
persistent currents in mesoscopic conducting rings. Here we analyze their
dependence on magnetic flux with emphasis on identifying possibilities to prove
the presence and extract the strength of Rashba spin splitting in
low-dimensional systems. Effects of disorder and mixing between
quasi-onedimensional ring subbands are considered. The spin-orbit coupling
strength can be inferred from the values of flux where sign changes occur in
the persistent charge current. As an important consequence of the presence of
spin splitting, we identify a nontrivial persistent spin current that is not
simply proportional to the charge current. The different flux dependences of
persistent charge and spin currents are a unique signature of spin-orbit
coupling affecting the electronic structure of the ring.
