706 research outputs found

    Dephasing due to electron-electron interaction in a diffusive ring

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    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 nn of the magnetoconductivity. Whereas phase coherence relaxation is non exponential for the harmonic n=0n=0, it is always exponential for harmonics n≠0n\neq0. 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

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    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

    Weak localization in multiterminal networks of diffusive wires

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    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

    Derivation of the Zakharov equations

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    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

    Conditional stability of unstable viscous shock waves in compressible gas dynamics and MHD

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    Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic--parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small L1∩H3L^1\cap H^3 perturbations, converging time-asymptotically to a translate of the unperturbed wave. That is, for a shock with pp unstable eigenvalues, we establish conditional stability on a codimension-pp manifold of initial data, with sharp rates of decay in all LpL^p. For p=0p=0, we recover the result of unconditional stability obtained by Mascia and Zumbrun. The main new difficulty in the hyperbolic--parabolic case is to construct an invariant manifold in the absence of parabolic smoothing.Comment: 32p

    Quantum oscillations in mesoscopic rings and anomalous diffusion

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    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

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    We investigate weak localization in metallic networks etched in a two dimensional electron gas between 25 25\:mK and 750 750\: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 T≳0.3 T\gtrsim0.3\: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

    Direct measurement of the phase coherence length in a GaAs/GaAlAs square network

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    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 lengthL_ϕL\_{\phi} in units of the lattice length without any adjustableparameters.We use this method to determine L_ϕL\_{\phi} in a network realised from a 2Delectron gas (2DEG) in a GaAS/GaAlAs heterojunction. The temperaturedependence follows a power law T−1/3T^{-1/3} 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
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