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A quantum kinetic theory of the linear response to an electric field is provided from a controlled expansion of the Keldysh theory at leading order, for a multiband electron system with weak scalar disorder. The response is uniquely partitioned into intraband distribution functions and interband quantum coherences. A new explicit formula is provided for the latter, outlining their true nature as local dependent quantities, for which the mesoscopic gradients of the former is uncovered as a source term, opening a new research area. The precise connection with the Kubo formula in the ladder approximation is established. A pedagogical application to spin-orbit torque theory in the two dimensional electron gas demonstrates the striking efficiency of the quantum kinetic approach. Some important implications for the theory of orbital transport are also briefly discussed., Comment: Accepted on PRB Letters, https://journals.aps.org/prb/accepted/0b072Y0bL5817a8e81174bb7c6101616a1ed72697

We study the dynamics of the collision of two solitary waves for the Zakharov-Kuznetsov equation in dimension $2$ and $3$. We describe the evolution of the solution behaving as a sum of $2$-solitary waves of nearly equal speeds at time $t=-\infty$ up to time $t=+\infty$. We show that this solution behaves as the sum of two modulated solitary waves and an error term which is small in $H^1$ for all time $t \in \mathbb R$. Finally, we also prove the stability of this solution for large times around the collision. The proofs are a non-trivial extension of the ones of Martel and Merle for the quartic generalized Korteweg-de Vries equation to higher dimensions. First, despite the non-explicit nature of the solitary wave, we construct an approximate solution in an intrinsic way by canceling the error to the equation only in the natural directions of scaling and translation. Then, to control the difference between a solution and the approximate solution, we use a modified energy functional and a refined modulation estimate in the transverse variable. Moreover, we rely on the hamiltonian structure of the ODE governing the distance between the waves, which cannot be approximated by explicit solutions, to close the bootstrap estimates on the parameters. We hope that the techniques introduced here are robust and will prove useful in studying the collision phenomena for other focusing non-linear dispersive equations with non-explicit solitary waves., Comment: 72 pages, 4 figures

We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov-Kuznetsov equation in dimensions two and three. Moreover, we derive a qualitative version of the orbital stability result which turns out to be useful for the study of the collision of two solitary waves. The proof extends the ideas of Martel, Merle and Tsai for the sub-critical gKdV equation in dimension one to the higher-dimensional case. It relies on monotonicity properties on oblique half-spaces and rigidity properties around one solitary wave introduced by C\^ote, Mu\~noz, Pilod and Simpson in dimension two, and by Farah, Holmer, Roudenko and Yang in dimension three., Comment: 32 pages, 7 figures

Starting from the Keldysh theory, for a general low energy $N$-band Hamiltonian in the clean limit, we perform a manifestly $\smash{U(1) \times SU(N)}$ gauge invariant semiclassical expansion. A generalized Berry curvature tensor is shown to control a redistribution of spectral weights. New expressions for certain physical quantities ensue, establishing the limits of a previously proposed correction to the density of states. In the two-band case, we derive a completely general semiclassical kinetic theory including all $O(\hbar)$ quantum corrections. As an application, we show how one can recover, out of a single simple calculation, the chiral anomaly, intrinsic anomalous Hall conductivity and chiral magnetic effect, in all generality. The demonstrated flexibility and efficiency of our formalism derives from the insulation it provides from the underlying complexity of the quantum kinetics, notwithstanding its rigorous connection to this deeper level., Comment: Final version, including in particular i) a more pedagogical presentation of the theoretical underpinning of our theory, ii) a revised application section providing a unified derivation of the chiral anomaly, intrinsic anomalous hall effect and chiral magnetic effect for a general two-band Hamiltonian

We study the solitary waves of fractional Korteweg-de Vries type equations, that are related to the $1$-dimensional semi-linear fractional equations: \begin{align*} \vert D \vert^\alpha u + u -f(u)=0, \end{align*} with $\alpha\in (0,2)$, a prescribed coefficient $p^*(\alpha)$, and a non-linearity $f(u)=\vert u \vert^{p-1}u$ for $p\in(1,p^*(\alpha))$, or $f(u)=u^p$ with an integer $p\in[2;p^*(\alpha))$. Asymptotic developments of order $1$ at infinity of solutions are given, as well as second order developments for positive solutions, in terms of the coefficient of dispersion $\alpha$ and of the non-linearity $p$. The main tools are the kernel formulation introduced by Bona and Li, and an accurate description of the kernel by complex analysis theory.

We study one particular asymptotic behaviour of a solution of the fractional modified Korteweg-de Vries equation (also known as the dispersion generalised modified Benjamin-Ono equation): \begin{align}\tag{fmKdV} \partial_t u + \partial_x (-\vert D \vert^\alpha u + u^3)=0. \end{align} The dipole solution is a solution behaving in large time as a sum of two strongly interacting solitary waves with different signs. We prove the existence of a dipole for fmKdV. A novelty of this article is the construction of accurate profiles. Moreover, to deal with the non-local operator $\vert D \vert^\alpha$, we refine some weighted commutator estimates.

We study here the Zakharov-Kuznetsov equation in dimension $2$ and $3$ and the modified Zakharov-Kuznetsov equation in dimension $2$. Those equations admit solitons, characterized by their velocity and their shift. Given the parameters of $K$ solitons $R^k$ (with distinct velocities), we prove the existence and uniqueness of a multi-soliton $u$ such that $\left\| u- \sum_{k=1}^K R^k \right\|_{H^1}\rightarrow 0 $ as $t \rightarrow +\infty$. The convergence takes place in $H^s$ with an exponential rate for all $s\geq 0$. The construction is made by successive approximations of the multi-soliton. We use classical arguments to control of $H^1$-norms of the errors (inspired by Martel [21]), and introduce a new ingredient for the control of the $H^s$-norm in dimension $d \geq2$, by a technique close to monotonicity.

We consider the Zakharov-Kuznetsov equation (ZK) in space dimension 2. Solutions u with initial data u\_0 $\in$ H s are known to be global if s $\ge$ 1. We prove that for any integer s $\ge$ 2, u(t) H s grows at most polynomially in t for large times t. This result is related to wave turbulence and how a solution of (ZK) can move energy to high frequencies. It is inspired by analoguous results by Staffilani on the non linear Schr{\"o}dinger Korteweg-de-Vries equation. The main ingredients are adequate bilinear estimates in the context of Bourgain's spaces.

A biomimetic model of cell-cell communication was developed to probe the passive molecular transport across ion channels inserted in synthetic lipid bilayers formed between contacting droplets arranged in a linear array. Diffusion of a fluorescent probe across the array was measured for different pore concentrations. The diffusion characteristic time scale is found to vary non-linearly with the pore concentration. Our measurements are successfully modeled by a continuous time random walk description, whose waiting time is the first exit time from a droplet through a cluster of pores. The size of the cluster of pores is found to increase with their concentration. Our results provide a direct link between the mesoscopic permeation properties and the microscopic characteristics of the pores such as their number, size and spatial arrangement., Comment: 5 pages, 3 figures

We have developed a method to produce aqueous microdroplets in an oil phase, based on the periodic extraction of a pending droplet across the oil/air interface. This interface forms a capillary trap inside which a droplet can be captured and detached. This process is found to be capillary- based and quasi-static. The droplet size and emission rate are independently governed by the injected volume per cycle and the extraction frequency. We find that the minimum droplet diameter is close to the injection glass capillary diameter and that variations in surface tension moderately perturb the droplet size. A theoretical model based on surface energy minimization in the oil/water/air phases was derived and captures the experimental results. This method enables robust, versatile and tunable production of microdroplets at low production rates.

Topological magnetic textures - like skyrmions - have become a major player in the design of next-generation magnetic storage technology due to their stability and the control of their motion by ultra-low current densities. A major challenge to develop this new skyrmion-based technology is to achieve the controlled and deterministic creation of magnetic skyrmions without the need of complex setups. We demonstrate a solution to this challenge by showing how to create skyrmions and other magnetic textures in ferromagnetic thin films by means of a homogeneous DC current and without requiring Dzyaloshinskii-Moriya interactions. This is possible by exploiting a static loss of stability arising from the interplay of current-induced spin-transfer torque and a spatially inhomogeneous magnetization, which can be achieved, e.g., by locally engineering the anisotropy, the magnetic field, or other magnetic interactions. The magnetic textures are created controllably, efficiently, and periodically with a period that can be tuned by the applied current strength. We propose specific experimental setups realizable with simple materials, such as cobalt based materials, to observe the periodic formation of skyrmions. We show that adding chiral interactions will not influence the basics of the generations but then influence the consequent dynamics with respect to the stabilization of topological textures. Our findings allow for the production of skyrmions on demand in simple ferromagnetic thin films by homogeneous DC currents., Comment: 21 pages, 7 figures; 12 pages supplementary material, 4 supplementary figures

We predict the electrical generation and injection of domain walls into a ferromagnetic nano-wire without the need of an assisting magnetic field. Our analytical and numerical results show that above a critical current $j_{c}$ domain walls are injected into the nano-wire with a period $T \sim (j-j_{c})^{-1/2}$. Importantly, domain walls can be produced periodically even in a simple exchange ferromagnet with uniaxial anisotropy, without requiring any standard "twisting" interaction like Dzyaloshinskii-Moriya or dipole-dipole interactions. We show analytically that this process and the period exponents are universal and do not depend on the peculiarities of the microscopic Hamiltonian. Finally we give a specific proposal for an experimental realization., Comment: 7 pages, 3 figures; this article supersedes arXiv:1512.00784

We report a study on the complete spin-wave spectrum inside a vortex state nano-disk. Transformation of this spectrum is continuously monitored as the nano-disk becomes gradually magnetized by a perpendicular magnetic field and encouters a second order phase transition to the uniformly magnetized state. This reveals the bijective relationship that exists between the eigen-modes in the vortex state with the ones in the saturated state. It is found that the gyrotropic mode can be continuously viewed as a uniform phase precession, which uniquely softens (its frequency vanishes) at the saturation field to transform above into the Kittel mode. By contrast the other spin-wave modes remain finite as a function of the applied field while their character is altered by level anti-crossing.

We investigated the viscoelastic response of model interphase chromosomes by tracking the three-dimensional motion of hundreds of dispersed Brownian particles of sizes ranging from the thickness of the chromatin fiber up to slightly above the mesh size of the chromatin solution. In agreement with previous computational studies on polymer solutions and melts, we found that the large-time behaviour of diffusion coefficient and the experienced viscosity of moving particles as functions of particle size deviate from the traditional Stokes-Einstein relation, and agree with a recent scaling theory of diffusion of non-sticky particles in polymer solutions. Interestingly, we found that at short times large particles are temporary "caged" by chromatin spatial constraints, which thus form effective domains whose size match remarkably well recent experimental results for micro-tracers inside interphase nuclei. Finally, by employing a known mathematical relation between the time mean-square displacement of tracked particles and the complex shear modulus of the surrounding solution, we calculated the elastic and viscous moduli of interphase chromosomes., Comment: 10 pages, 6 figures, accepted for publication in Journal of Chemical Physics

The spin Hall effect (SHE), induced by spin-orbit interaction in nonmagnetic materials, is one of the promising phenomena for conversion between charge and spin currents in spintronic devices. The spin Hall (SH) angle is the characteristic parameter of this conversion. We have performed experiments of the conversion from spin into charge currents by the SHE in lateral spin valve structures. We present experimental results on the extrinsic SHEs induced by doping nonmagnetic metals, Cu or Ag, with impurities having a large spin-orbit coupling, Bi or Pb, as well as results on the intrinsic SHE of Au. The SH angle induced by Bi in Cu or Ag is negative and particularly large for Bi in Cu, 10 times larger than the intrinsic SH angle in Au. We also observed a large SH angle for CuPb but the SHE signal disappeared in a few days. Such an aging effect could be related to a fast mobility of Pb in Cu and has not been observed in CuBi alloys., Comment: 12 pages, 10 figures

We demonstrate that a giant spin Hall effect (SHE) can be induced by introducing a small amount of Bi impurities in Cu. Our analysis based on a new 3-dimensional finite element treatment of spin transport shows that the sign of the SHE induced by the Bi impurities is negative and its spin Hall (SH) angle amounts to -0.24. Such a negative large SH angle in CuBi alloys can be explained by applying the resonant scattering model proposed by Fert and Levy [Phys. Rev. Lett. 106, 157208 (2011)] to 6p impurities., Comment: 5 pages, 4 figures

In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process., Comment: 132 pages, r\'edaction non termin\'ee, synth\`ese de travail de recherche doctorale

In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process., Comment: 13 pages

We report on a spectroscopic study of the spin-wave eigen-modes inside an individual normally magnetized two layers circular nano-pillar (Permalloy$|$Copper$|$Permalloy) by means of a Magnetic Resonance Force Microscope (MRFM). We demonstrate that the observed spin-wave spectrum critically depends on the method of excitation. While the spatially uniform radio-frequency (RF) magnetic field excites only the axially symmetric modes having azimuthal index $\ell=0$, the RF current flowing through the nano-pillar, creating a circular RF Oersted field, excites only the modes having azimuthal index $\ell=+1$. Breaking the axial symmetry of the nano-pillar, either by tilting the bias magnetic field or by making the pillar shape elliptical, mixes different $\ell$-index symmetries, which can be excited simultaneously by the RF current. Experimental spectra are compared to theoretical prediction using both analytical and numerical calculations. An analysis of the influence of the static and dynamic dipolar coupling between the nano-pillar magnetic layers on the mode spectrum is performed.

We show that a model, recently used to describe all the dynamical regimes of the magnetic field generated by the dynamo effect in the VKS experiment [1], also provides a simple explanation of the reversals of Earth's magnetic field, despite strong differences between both systems., Comment: update version, with new figures

The spin-transfer effect has been studied in magnetic tunnel junctions (PtMn/CoFe/Ru/CoFe/Al2O3/CoFe/NiFe) with dimensions down to 0.1x0.2 um2 and resistance-area product RA in the range of 0.5-10 Ohm m2 (dR/R=1-20%). Current-induced magnetization switching is observed with a critical current density of about 8e6 A/cm2. The attribution of the switching to the spin-transfer effect is supported by a current-induced dR/R value identical to the one obtained from the R versus H measurements. Furthermore, the critical switching current density has clear dependence on the applied magnetic field, consistent with what has been observed previously in the case of spin-transfer induced switching in metallic multilayer systems.

The spin transfer switching current distribution within a cell was studied in magnetic tunnel junction based structures having alumina barriers with resistance-area product (RA) of 10 to 30 Ohm-um2 and tunneling magneto-resistance (TMR) of ~20%. These were patterned into current perpendicular to plane configured nano-pillars having elliptical cross-sections of area ~0.02 um2. The width of the critical current distribution (sigma/average of distribution), measured using 30 ms current pulse width, was found to be 7.5% and 3.5% for cells with thermal factor (KuV/kBT) of 40 and 65 respectively. The distribution width did not change significantly for pulse widths between 1 s and 4 ms. An analytical expression for probability density function, p(I/Ico) was derived considering the thermally activated spin transfer model, which supports the experimental observation that the thermal factor is the most significant parameter in determining the within cell critical current distribution width., Comment: 12 pages, 4 figures