Non-equilibrium charge noise and dephasing from a spin-incoherent Luttinger liquid

We theoretically investigate the charge noise and dephasing in a metallic device in close proximity to a spin incoherent Luttinger liquid with a small but finite current. The frequency dependence of the charge noise exhibits a loss of frequency peaks corresponding to the $2k_F$ part of the density correlations in the electron liquid when the temperature $T$ is increased from values below the magnetic exchange energy $J$ of the electron gas to values above it. The dephasing rate in a nearby metallic nanostructure also shows a cross-over for $T \sim J$ and may exhibit a non-monotonic temperature dependence. For a range of temperatures the dephasing rate {\em decreases} with increasing temperatures. The proposed experiments provide a convenient approach to probe the spin-incoherent Luttinger liquid and should be implementable in a wide variety of systems.