Static Conductance and Scaling Theory of Localization in One Dimension

It is shown that the Ohmic dc conductance of a one-dimensional system equals to either Gₚ=(e²π)T or Gc=(e²π)T(1-T), depending on whether the system is connected to a perfect one-dimensional conductor or to a classical wire (behaving as a current source), respectively. The parameter β≡d〈lng^'〉dlnL, where L is the length of the system, depends only on 〈lng^'〉, so that β=〈lng^'〉, with g^'=(πe²)Gₚ.