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 〈 Δ g 2 〉 = 8 / 15 (e 2 / h) 2 in one dimension. • The theory of transport in metals provides the conductance correlation function. • Its generalization in a magnetic field does not agree with the conventional theory. • The conductance correlation function in a magnetic field is corrected in this work. • The exact correlation function is derived for a quasi-one-dimensional material. • 〈 Δ g 2 〉 in one dimension is provided. [ABSTRACT FROM AUTHOR]