Transport through short quantum wires

At temperatures $T < {\hbar v_F}/{K_B d} \equiv T^{wire}$ the collective excitations are negligible and the spectrum of the short wire is dominated by the ''zero modes'' particle excitations. At temperature $ T > T^{wire}$ a spin polarized state controlled by the electron-electron interaction and electron density is identified at short times. As a result the anomaly in the conductance $G > 2 \times 0.5 {e^2}/{h} $ appears. At $T \to 0$ by varying the gate voltage we find that our problem is equivalent to a resonant impurity level. As a result perfect transmission with a conductance $G \simeq \frac{2 e^2}{h}$ is obtained. The model presented here can be used as a spin filter which operate by varying the temperature. Transport through a short quantum wire with electron-electron interaction and length ``$d$'' coupled to Luttinger leads is considered. The short wire model might explain the ``0.7 anomaly'' observed in quantum point contacts.