This report is a summary of recent work on the properties of phase coherent diffusive conductors, especially in the geometry of networks — also called graphs — made of quasi-$\mathrm{1D}$ diffusive wires. These properties are written as a function of the spectral determinant of the diffusion equation (the product of its eigenvalues). For a network with $N$ nodes, this spectral determinant is related to the determinant of an $N\times N$ matrix which describes the connectivity of the network. I also consider the transmission through networks made of $\mathrm{1D}$ ballistic wires and show how the transmission coefficient can be written in terms of an $N\times N$ matrix very similar to the above one. Finally I present a few considerations on the relation between the magnetism of noninteracting systems and the magnetism of interacting diffusive systems.

%0 Journal Article
%T Mesoscopic physics on graphs
%A G. Montambaux
%I Physics-Uspekhi
%D 2001
%J Phys. Usp.
%V 44
%N 13
%P 65-68
%U https://ufn.ru/en/articles/2001/13/m/
%U https://doi.org/10.1070/1063-7869/44/10S/S13