The magic of Feynman’s QED: from field-less electrodynamics to the Feynman diagrams

For some time, even after the Feynman diagrams and rules were publicly known, the foundations of Feynman’s quantum electrodynamics remained mostly private. Its stupendous efficiency then appeared like magic to most of his competitors. The purpose of this essay is to reveal the hidden contrivances of this magic, in a journey from field-less electrodynamics to the Feynman diagrams.

     

Electron density characterization by use of a broadband x-ray-compatible wave-front sensor

The use of a Hartmann wave-front sensor to accurately measure the line-integrated electron density gradients formed in laser-produced and z-pinch plasma experiments is examined. This wave-front sensor may be used with a soft-x-ray laser as well as with incoherent line emission at multikilovolt x-ray energies. This diagnostic is significantly easier to use than interferometery and moiré deflectometry, both of which have been demonstrated with soft-x-ray lasers. This scheme is experimentally demonstrated in the visible region by use of a Shack-Hartmann wave-front sensor and a liquid-crystal spatial light modulator to simulate a phase profile that could occur when an x-ray probe passes through a plasma. The merits of using a Hartmann sensor include a wide dynamic range, broadband or low-coherence-length light capability, high x-ray efficiency, two-dimensional gradient determination, multiplexing capability, and experimental simplicity. Hartmann sensors could also be utilized for wavelength testing of extreme-ultraviolet lithography components and x-ray phase imaging of biological specimens.     

Pressure Boundary Conditions for Blood Flows

Simulations of blood flows in arteries require numerical solutions of fluid-structure interactions involving Navier-Stokes equations coupled with large displacement visco-elasticity for the vessels. Among the various simplifications which have been proposed, the surface pressure model leads to a hierarchy of simpler models including one that involves only the pressure. The model exhibits fundamental frequencies which can be computed and compared with the pulse. Yet unconditionally stable time discretizations can be constructed by combining implicit time schemes with Galerkin-characteristic discretization of the convection terms in the Navier-Stokes equations. Such problems with prescribed pressure on the walls will be shown to be efficient and accurate as an approximation of the full fluid structure interaction problem.     

Cyclic sieving,rotation, and geometric representation theory

We study rotation of invariant vectors in tensor products of minuscule representations. We define a combinatorial notion of rotation of minuscule Littelmann paths. Using affine Grassmannians, we show that this rotation action is realized geometrically as rotation of components of the Satake fiber. As a consequence, we have a basis for invariant spaces, which is permuted by rotation (up to global sign). Finally, we diagonalize the rotation operator by showing that its eigenspaces are given by intersection homology of quiver varieties. As a consequence, we generalize Rhoades’ work on the cyclic sieving phenomenon.     

The quantum drift-diffusion model: Existence and exponential convergence to the equilibrium

This work is devoted to the analysis of the quantum drift-diffusion model derived by Degond et al. in [7]. The model is obtained as the diffusive limit of the quantum Liouville–BGK equation, where the collision term is defined after a local quantum statistical equilibrium. The corner stone of the model is the closure relation between the density and the current, which is nonlinear and nonlocal, and is the main source of the mathematical difficulties. The question of the existence of solutions has been open since the derivation of the model, and we provide here a first result in a one-dimensional periodic setting. The proof is based on an approximation argument, and exploits some properties of the minimizers of an appropriate quantum free energy. We investigate as well the long time behavior, and show that the solutions converge exponentially fast to the equilibrium. This is done by deriving a non-commutative logarithmic Sobolev inequality for the local quantum statistical equilibrium.     

Optical and electrical properties of modulation-doped n and p-type Ga x In1-x N y As1-y /GaAs quantum wells for 1.3 μm laser applications

We present a comprehensive study of spectral photoluminescence (PL), photoconductivity and Hall mobility in undoped, n and p-type modulation-doped quantum wells of Ga_1-x In _x N _y As_1-y /GaAs with varying nitrogen concentration. We show that the increasing nitrogen composition red shifts the energy gap and this red shift is accompanied with a reduction of the 2D electron mobility in the quantum wells. True temperature dependence of the band gap, free from errors associated with nitrogen induced exciton trapping effects, is observed because in the modulation doped QW samples PL emission is dominated by band-to-band recombination and the S-shape temperature dependence is eliminated. Excellent fit to semi-experimental Varshni equation is obtained and the temperature dependence of the band gap in the linear regime (dE/dT) is tabulated as a function of nitrogen concentration and the type of dopant.     

Validation of molecular mass measurements by means of diffusion-ordered NMR spectroscopy: Application to oligosaccharides

The validation of molecular mass measurements by using DOSY spectrocopy is presented. A mixture of oligosaccharides has been studied and an extended model has been used. A method has been proposed and applied to correct the imperfections due either to the lock system or the room temperature regulator.     

57Fe Mössbauer study of a deposit in an industrial cooling circuit supplied with raw river water

In this work, the nature of the deposit found inside an industrial cooling circuit (which consists of a mixture of different iron containing phases) has been characterized in detail by ⁵⁷Fe Mössbauer spectroscopy. Electron Paramagnetic Resonance spectroscopy was also used to check for the presence of other metals, mainly manganese and copper, detected by the Inductive Coupled Plasma method. We conclude that the deposit contains a large amount of Fe(III), probably consisiting of ferrihydrite nanoparticles and of goethite, either bulk or as large particles. It also contains traces of an Fe(II) species (about 3%), probably adsorbed on the iron oxides. Mn(II) and traces of Cu(II) are also present.