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2001

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Quantum dots and wells, mesoscopic networks


Mesoscopic physics on graphs


Laboratoire de Physique des Solides, associe au CNRS Universite Paris-Sud, Bâtiment 510, Orsay, 91405, France , Orsay , France

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.

Fulltext pdf (166 KB)
Fulltext is also available at DOI: 10.1070/1063-7869/44/10S/S13
PACS: 73.63.−b, 73.21.−b, 68.65.−k, 71.35.−y (all)
DOI: 10.1070/1063-7869/44/10S/S13
URL: https://ufn.ru/en/articles/2001/13/m/
Citation: Montambaux G "Mesoscopic physics on graphs" Phys. Usp. 44 65–68 (2001)
BibTex BibNote ® (generic)BibNote ® (RIS)MedlineRefWorks
%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

Îðèãèíàë: Montambaux G «Mesoscopic physics on graphs» ÓÔÍ 171 65–68 (2001); DOI: 10.1070/1063-7869/44/10S/S13

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