Skip to Main content Skip to Navigation
Theses

Formules de courant dans les systèmes mésoscopiques

Abstract : The main topic of the thesis is the transport in mesoscopic systems. In the first part of the work, we study thecase of a connection through an adiabatic potential on a one dimensional system without initial distribution, wesaid a “partition-free approach”. It is shown that the full current is uniformly bounded with respect to theadiabatic speed of connection, when it goes to zero. We prove the existence of the linear part of the state andcurrent. The second part of the thesis has led to publication of an article and deals with the study of a discretemodel without initial distribution. We prove that in this system and after an electrochemical disturbance thereexists a nonequilibrium steady state, and the Landauer-Büttiker formula is demonstrated for this model.The last part of the thesis, which also has led to an article, concerns the study of the approximation of quantumwaveguides by quantum graphs. We are interested in a waveguide locally twisted. We studyminus theLaplacian on this locally twisted waveguide. When the diameter of the guide goes to zero and simultaneouslywhen the support of the twisting goes to zero, we prove that the limit graph is the straight line, and the limitoperator is minus the Laplacian on the straight line plus a Dirichlet condition at the origin. The Dirichletcondition is the consequence of the shrinking done. In the appendix, we
Document type :
Theses
Complete list of metadatas

Cited literature [66 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00680606
Contributor : Abes Star :  Contact
Submitted on : Monday, March 19, 2012 - 5:17:13 PM
Last modification on : Friday, May 17, 2019 - 8:21:00 AM
Long-term archiving on: : Wednesday, June 20, 2012 - 2:35:23 AM

File

these_gianeselloc.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-00680606, version 1

Citation

Céline Gianesello. Formules de courant dans les systèmes mésoscopiques. Mathématiques générales [math.GM]. Université de Toulon, 2011. Français. ⟨NNT : 2011TOUL0011⟩. ⟨tel-00680606⟩

Share

Metrics

Record views

560

Files downloads

460