  We consider theoretically spin correlations in an 1D quantum wire with
Rashba-Dresselhaus spin-orbit interaction (RDI). The correlations of
non-interacting electrons display electron-spin resonance at a frequency
proportional to the RDI coupling. Interacting electrons on varying the
direction of external magnetic field transit from the state of Luttinger liquid
(LL) to the spin density wave (SDW) state. We show that the two-time total spin
correlations of these states are significantly different. In the LL the
projection of total spin to the direction of the RDI induced field is conserved
and the corresponding correlator is equal to zero. The correlators of two
components perpendicular to the RDI field display a sharp ESR driven by RDI
induced intrinsic field. In contrast, in the SDW state the longitudinal
projection of spin dominates, whereas the transverse components are suppressed.
This prediction indicates a simple way for experimental diagnostic of the SDW
in a quantum wire.
