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Spin-orbit and impurity scattering in an integrable electron model: Exact results for dynamic correlations

We introduce an integrable model of spin-polarized interacting electrons subject to a spin-conserving spin-orbit interaction. Using Bethe Ansatz and conformal field theory we calculate the exact large-time single-electron and density correlations and find that while the spin-orbit interaction enhances the single-electron Green's function, the density correlations get suppressed. Adding a localized impurity and coupling it to the electrons so that integrability is preserved, the dynamic correlations are found to change significantly after a quantum quench with the impurity interaction switched on suddenly. When the electrons are confined to a periodic structure, the correlations are indifferent to the location of the impurity and only carry an imprint of its intrinsic properties. We conjecture that this unusual feature originates from the integrability of the model.