Weak Localization in Electronic Transport in Mesoscopic Systems

The present study focuses on the description of ballistic electronic transport in nanostructured systems, with a particular focus on the semiclassical description and weak localization corrections of the first cumulants (such as conductance, shot-noise power, and higher orders) of the charge count statistics. In the context of ballistic quantum dot networks, efficient implementation methods are scarce. In this context, the present work proposes an approach based on the extension of Y. Nazarov's quantum circuit theory combined with graph theory in terms of the weighted adjacency matrix of conductances between the quantum dots in the network. This reduction in computational cost enables the investigation of the impact of topology on the cumulants of the charge count statistics in these systems.

This approach is applied through an investigation of the ballistic-diffusive transition. This investigation involves the behavior of the first cumulants in planar graphs and certain distribution profiles of the transparency of the contacts between quantum dots in the network.

Consequently, this study has expanded our comprehension of electronic transport in nanostructures and has presented promising prospects for the implementation of crossover parameters between Wigner-Dyson universality classes.