Interacting electrons with spin in a one-dimensional dirty wire connected to leads

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 sp in parts of an incident electron even in the noninteracting leads. The Four ier transforms of nonlocal correlation functions is computed for T>>omega. In particular, this allows to study the proximity effect, related to the An dreev reflection. In addition, a new type of proximity effect emerges when the wire has normally a tendency towards Wigner crystal formation. The latt er is suppressed by the leads below a space-dependent crossover temperature ; it gets dominated everywhere by the 2k(F) charge-density wave at T<L-(3/2 (K-l)) for short-range interactions with parameter K<1/3. The lowest-order renormalization equations of a weak backscattering potential are derived ex plicitly at finite temperature. A perturbative expression for the conductan ce in the presence of a potential with arbitrary spatial extension is given . It depends on the interactions, but is also affected by the noninteractin g leads, especially for very repulsive interactions, K< 1/3. This leads to various regimes, depending on temperature and on K. For randomly distribute d weak impurities, die conductance fluctuations, equal to that of R=g-2e(2) /h, are computed. They depend on die interaction parameters, and are differ ent for electrons with or without spin. But the ratio Var(R)/R-2 stays alwa ys of the same order: it is equal to L-T/L<<1 in the high-temperature limit , then saturates at 1/2 in the low-temperature limit, indicating that the r elative fluctuations of R are universal. [S0163-1829(98)09831-2].