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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, Франция

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.

Текст pdf (166 Кб)
English fulltext is available at DOI: 10.1070/1063-7869/44/10S/S13
PACS: 73.63.−b, 73.21.−b, 68.65.−k, 71.35.−y (все)
DOI: 10.1070/1063-7869/44/10S/S13
URL: https://ufn.ru/ru/articles/2001/13/m/
Цитата: Montambaux G "Mesoscopic physics on graphs" УФН 171 65–68 (2001)
BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks
Русский English
PT Journal Article
TI Mesoscopic physics on graphs
AU Montambaux G
FAU Montambaux G
DP 10 Sup, 2001
TA Usp. Fiz. Nauk
VI 171
IP 13
PG 65-68
RX 10.1070/1063-7869/44/10S/S13
URL https://ufn.ru/ru/articles/2001/13/m/
SO Usp. Fiz. Nauk 2001 Sup 10;171(13):65-68

English citation: Montambaux G “Mesoscopic physics on graphsPhys. Usp. 44 65–68 (2001); DOI: 10.1070/1063-7869/44/10S/S13

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