Conductance of a Finite Quantum Wire Connected to Reservoirs

Abstract

We study a finite quantum wire connected to external leads, and show that the conductance of the system significantly depends upon the length of the quantum wire and the position of the impurity in it. For a very long quantum wire and the impurity far away from its two ends, the conductance has the same behavior as that for an infinity quantum wire above some very little energy scale. However, for a very short quantum wire, the conductance is independent of the electron-electron interactions in it and closing to $e^{2}/(2\pi\hbar)$ in a higher temperature range. While, in a lower temperature range, the conductance shows the same property as that for an infinity quantum wire.