Exact correlation function of the conductance in weakly disordered quasi-one-dimensional material

Fluctuations in the conductance are due to quantum diffusion through impurities in materials. If the material is weakly disordered, and if the size where current flows is smaller than the localization length, the conductance fluctuates around a universal value. This phenomenon is known as Universal Conductance Fluctuation (UCF). The fluctuations in the conductance are measured by the correlation function of the conductance, which can be evaluated diagrammatically. The expressions for the correlation function of the conductance from the conventional theory of transport in metals and its generalization in a strong magnetic field are revisited. An exact solution is provided for both expressions. We show that the exact value of the statistical variance of the conductance is (Ag2) = 8/15(e2/h)2 in one dimension.