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.

RT Journal
T1 Mesoscopic physics on graphs
A1 Montambaux,G.
PB Успехи физических наук
PY 2001
FD 10 Sup, 2001
JF Успехи физических наук
JO Усп. физ. наук
VO 171
IS 13
SP 65-68
DO 10.1070/1063-7869/44/10S/S13
LK https://ufn.ru/ru/articles/2001/13/m/