Tunneling conductance of a mesoscopic ring with spin-orbit coupling and   Tomonaga-Luttinger interaction
  We study the tunneling current through a mesoscopic two-terminal ring with spin-orbit coupling, which is threaded by a magnetic flux. The electron-electron interaction in the ring is described in terms of a Tomonaga-Luttinger model which also allows us to account for a capacitive coupling between the ring and the gate electrode. In the regime of weak tunneling, we describe how, at temperatures lower than the mean level spacing, the peak positions of the conductance depend on magnetic flux, spin-orbit coupling strength, gate voltage, charging energy, and interaction parameters (charge and spin velocity and stiffness). 
M. Pletyukhov, V. Gritsev, and N. Pauget