721 research outputs found
On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach
We consider a metric graph made of two graphs
and attached at one point. We derive a formula relating the
spectral determinant of the Laplace operator
in terms of the spectral
determinants of the two subgraphs. The result is generalized to describe the
attachment of graphs. The formulae are also valid for the spectral
determinant of the Schr\"odinger operator .Comment: LaTeX, 8 pages, 7 eps figures, v2: new appendix, v3: discussions and
ref adde
Dephasing due to electron-electron interaction in a diffusive ring
We study the effect of the electron-electron interaction on the weak
localization correction of a ring pierced by a magnetic flux. We compute
exactly the path integral giving the magnetoconductivity for an isolated ring.
The results are interpreted in a time representation. This allows to
characterize the nature of the phase coherence relaxation in the ring. The
nature of the relaxation depends on the time regime (diffusive or ergodic) but
also on the harmonics of the magnetoconductivity. Whereas phase coherence
relaxation is non exponential for the harmonic , it is always exponential
for harmonics . Then we consider the case of a ring connected to
reservoirs and discuss the effect of connecting wires. We recover the behaviour
of the harmonics predicted recently by Ludwig & Mirlin for a large perimeter
(compared to the Nyquist length). We also predict a new behaviour when the
Nyquist length exceeds the perimeter.Comment: 21 pages, RevTeX4, 8 eps figures; version of 10/2006 : eqs.(100-102)
of section V.C correcte
Effect of connecting wires on the decoherence due to electron-electron interaction in a metallic ring
We consider the weak localization in a ring connected to reservoirs through
leads of finite length and submitted to a magnetic field. The effect of
decoherence due to electron-electron interaction on the harmonics of AAS
oscillations is studied, and more specifically the effect of the leads. Two
results are obtained for short and long leads regimes. The scale at which the
crossover occurs is discussed. The long leads regime is shown to be more
realistic experimentally.Comment: LaTeX, 4 pages, 4 eps figure
Derivation of the Zakharov equations
This paper continues the study of the validity of the Zakharov model
describing Langmuir turbulence. We give an existence theorem for a class of
singular quasilinear equations. This theorem is valid for well-prepared initial
data. We apply this result to the Euler-Maxwell equations describing
laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic
estimate that describes solutions of the Euler-Maxwell equations in terms of
WKB approximate solutions which leading terms are solutions of the Zakharov
equations. Because of transparency properties of the Euler-Maxwell equations,
this study is led in a supercritical (highly nonlinear) regime. In such a
regime, resonances between plasma waves, electromagnetric waves and acoustic
waves could create instabilities in small time. The key of this work is the
control of these resonances. The proof involves the techniques of geometric
optics of Joly, M\'etivier and Rauch, recent results of Lannes on norms of
pseudodifferential operators, and a semiclassical, paradifferential calculus
Weak localization in multiterminal networks of diffusive wires
We study the quantum transport through networks of diffusive wires connected
to reservoirs in the Landauer-B\"uttiker formalism. The elements of the
conductance matrix are computed by the diagrammatic method. We recover the
combination of classical resistances and obtain the weak localization
corrections. For arbitrary networks, we show how the cooperon must be properly
weighted over the different wires. Its nonlocality is clearly analyzed. We
predict a new geometrical effect that may change the sign of the weak
localization correction in multiterminal geometries.Comment: 4 pages, LaTeX, 4 figures, 8 eps file
Quantum oscillations in mesoscopic rings and anomalous diffusion
We consider the weak localization correction to the conductance of a ring
connected to a network. We analyze the harmonics content of the
Al'tshuler-Aronov-Spivak (AAS) oscillations and we show that the presence of
wires connected to the ring is responsible for a behaviour different from the
one predicted by AAS. The physical origin of this behaviour is the anomalous
diffusion of Brownian trajectories around the ring, due to the diffusion in the
wires. We show that this problem is related to the anomalous diffusion along
the skeleton of a comb. We study in detail the winding properties of Brownian
curves around a ring connected to an arbitrary network. Our analysis is based
on the spectral determinant and on the introduction of an effective perimeter
probing the different time scales. A general expression of this length is
derived for arbitrary networks. More specifically we consider the case of a
ring connected to wires, to a square network, and to a Bethe lattice.Comment: 17 pages, 7 eps figure
Geometrical dependence of decoherence by electronic interactions in a GaAs/GaAlAs square network
We investigate weak localization in metallic networks etched in a two
dimensional electron gas between mK and mK when electron-electron
(e-e) interaction is the dominant phase breaking mechanism. We show that, at
the highest temperatures, the contributions arising from trajectories that wind
around the rings and trajectories that do not are governed by two different
length scales. This is achieved by analyzing separately the envelope and the
oscillating part of the magnetoconductance. For K we find
\Lphi^\mathrm{env}\propto{T}^{-1/3} for the envelope, and
\Lphi^\mathrm{osc}\propto{T}^{-1/2} for the oscillations, in agreement with
the prediction for a single ring \cite{LudMir04,TexMon05}. This is the first
experimental confirmation of the geometry dependence of decoherence due to e-e
interaction.Comment: LaTeX, 5 pages, 4 eps figure
Functionals of the Brownian motion, localization and metric graphs
We review several results related to the problem of a quantum particle in a
random environment.
In an introductory part, we recall how several functionals of the Brownian
motion arise in the study of electronic transport in weakly disordered metals
(weak localization).
Two aspects of the physics of the one-dimensional strong localization are
reviewed : some properties of the scattering by a random potential (time delay
distribution) and a study of the spectrum of a random potential on a bounded
domain (the extreme value statistics of the eigenvalues).
Then we mention several results concerning the diffusion on graphs, and more
generally the spectral properties of the Schr\"odinger operator on graphs. The
interest of spectral determinants as generating functions characterizing the
diffusion on graphs is illustrated.
Finally, we consider a two-dimensional model of a charged particle coupled to
the random magnetic field due to magnetic vortices. We recall the connection
between spectral properties of this model and winding functionals of the planar
Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and
conclusion added. Several references adde
Direct measurement of the phase coherence length in a GaAs/GaAlAs square network
The low temperature magnetoconductance of a large array of quantum
coherentloops exhibits Altshuler-Aronov-Spivak oscillations which
periodicitycorresponds to 1/2 flux quantum per loop.We show that the
measurement of the harmonics content in a square networkprovides an accurate
way to determine the electron phase coherence length in units of the
lattice length without any adjustableparameters.We use this method to determine
in a network realised from a 2Delectron gas (2DEG) in a GaAS/GaAlAs
heterojunction. The temperaturedependence follows a power law from
1.3 K to 25 mK with nosaturation, as expected for 1D diffusive electronic
motion andelectron-electron scattering as the main decoherence mechanism.Comment: Additional experimental data in version
Synthèse du colloque international sur la microfinance.
La microfinance a fait l’objet d’un colloque organisé par la Banque de France en juillet 2011. Les participants ont souligné son utilité comme outil d’inclusion financière, de développement économique et de lutte contre la pauvreté en s’appuyant sur les expériences des pays du Sud et ont proposé des pistes de réflexion pour le financement de son développement, ainsi que sur la pertinence et les modalités de sa régulation.microfinance, microcrédit, entrepreneuriat, lutte contre la pauvreté, régulation, réglementation, inclusion financière, développement économique.
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