  The Josephson current through a 1D quantum wire with Rashba spin-orbit and
electron-electron interactions is calculated. We show that the interplay of
Rashba and Zeeman interactions gives rise to a supercurrent through the 1D
conductor that is anomalous in the sense that it persists in the absence of any
phase difference between the two superconducting leads to which it is attached.
The electron dispersion asymmetry induced by the Rashba interaction in a
Luttinger-liquid wire plays a significant role for poorly transmitting
junctions. It is shown that for a weak or moderate electron-electron
interaction the spectrum of plasmonic modes confined to the normal part of the
junction becomes quasi-random in the presence of dispersion asymmetry.
