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Effects of interactions in mesoscopic systems

Abstract : In this thesis the effects of interactions between electrons
in mesoscopic systems are studied. One part is devoted to the study of mesoscopic super-conductors in which the size of the system is comparable to both coherence length and London penetration depth. In recent experiments performed on small aluminium disks the jumps of magnetisation as a function of external magnetic field were observed. We show that these jumps are due to the penetration of the magnetic field into the sample in the form of vortices and determine the number of vortices by solving the Ginzburg-Landau equations in some geometries analytically at the dual point and in the London regime. In both cases the resulting expressions for magnetisation are in good qualitative agreement with the experimental results. Magnetisation curves at the dual point are in good quantitative agreement with experiments, since this regime is relevant for the most experimental situations. The Ginzburg-Landau
equation in the London regime can be used to study the topology of
magnetic field profile. Each solution can be classified by the set of topological numbers (index), the number of vortices being one of
them. The topological study of the solutions of the Ginzburg-Landau
equations is not specific to the London regime and can be extended to other experimentally relevant regimes as well as to the more
complicated geometries of the sample.

Another part of this work deals with an interacting electrons in mesoscopic conductors. In parallel to the recent studies of such systems we study the localization in the Hilbert space of Tomonaga-Luttinger model. For the standard version of this model, the states are found to be extended in the basis of Slater determinants, representing the eigenstates of the non-interacting system. The linear dispersion which leads to the fact that these eigenstates are extended is replaced by one with random
level spacings modeling the complicated one-particle spectra of realistic models. The localization properties of the eigenstates are studied. The interactions are simplified and an effective one-dimensional Lloyd model is obtained. The effects of many-body energy correlations are studied numerically. The eigenstates of the system are found to be localized in Fock space for any strength of the interactions, but the localization is not exponential.
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Contributor : Dimitri Gangardt <>
Submitted on : Monday, May 5, 2003 - 9:42:17 AM
Last modification on : Monday, January 2, 2006 - 5:58:55 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:02:53 PM


  • HAL Id : tel-00002786, version 1


Dimitri Gangardt. Effects of interactions in mesoscopic systems. Superconductivity [cond-mat.supr-con]. Technion - Israel Institute of Technology, 2002. English. ⟨tel-00002786⟩



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