Hello! It seems that you are currently engaged in simulating the two-terminal conductance of a disordered conductor. I recommend that you proceed by implementing the code for the Landauer-Buttiker formula and the normalized localization length, which will provide you with a deeper understanding of the problem you are currently facing.
Q1: When disorder is included, it is essential to perform a disorder average over a series of different disorder configurations at a given disorder strength. When dealing with small systems, it is common for the standard error to be as large as the mean conductance, even when increasing the number of samples. In such cases, enlarging the system size can help mitigate the fluctuations and reduce the standard error. Q2: Yes, it does. If you calculate the normalized localization length of a disordered conductor, you will find that the localization length converges for a system as lengthy as 10^5~6. However, this would be computational expensive for simulating such a lengthy system. In the two-terminal conductance simulation using Landauer-Buttiker formula, you will need to set a proper length of the central scattering region to balance the precision and simulation time. On the other hand, there are series of length scale in quantum transport, such as the mean free path, phase coherence length, thermal length, etc., from which we define different transport regime. For example, when the mean free path is much larger than the system size, it is called ballistic regime, where each transmission channel contributes a Landauer conductance; if mean free path is smaller than the system size but larger than the phase coherence length, it is called (classical) diffusive regime; and if phase coherence length is larger than the mean free path, it is called quantum diffusive regime, where weak (anti-)localization effect is observed. In this case you may need to consider the conductivity rather than conductance cause it described ballistic tranport. Kwant provides kernel polynomial method implementation of Kubo-Bastin formula to calculate the londitudinal and Hall conductivity. I hope this can help you assist you in resolving the confusion or question you have. Best wishes, Peter
