Interacting electrons with spin in a one

We investigate a one-dimensional wire of interacting electrons connected to one-dimensional noninteracting leads in the absence and in the presence of a backscattering potential. The ballistic wire separates the charge and spin parts of an incident electron even in the noninteracting leads. The Fourier transform of nonlocal correlation functions are computed for T ≫ ω, allowing us to study the proximity effect related to Andreev reflection. A new type of proximity effect emerges when the wire tends towards Wigner crystal formation, which is suppressed by the leads below a space-dependent crossover temperature, becoming dominated by the 2 kF charge density wave for short range interactions with parameter K < 1/3 at T < L^{3/2}(K^{-1}). The lowest-order renormalization equations of a weak backscattering potential are derived explicitly at finite temperature, and a perturbative expression for the conductance in the presence of an arbitrary potential spatial extent is provided. This expression is influenced by interactions, especially for very repulsive interactions, leading to various regimes dependent on temperature and K. For randomly distributed weak impurities, the conductance fluctuations are calculated, with varying behavior depending on interaction parameters but consistent ratios in fluctuation behavior across temperature limits.