Les technologies quantiques

Quantum sensing with diamond

In these lectures I will introduce and explore properties of the Renormalisation Group (RG) both in its discrete and continuous forms. Topics to be discussed include multi scale expansions, the RG, Gaussian fixed points, Wick products from the RG point of view, ultraviolet cutoff removal, flow equations and perturbative flows, trivial and non-trivial fixed points, and critical field theories. Rigorous Discrete RG analysis. I will discuss a rigorous application for a non-trivial fixed point.

Polymer nanocomposites (PNCs) are made by dispersion of hard fillers in a polymer matrix, where the fillers are usually added to enhance mechanical properties. Such materials attract industrial interest and their investigation is essential for the improvement of their performances. The present study concerns nanocomposites obtained using hydrophilic silica nanoparticles (NPs) dispersed in a soft polymer matrix of styrene-butadiene, commonly used in car tire manufacturing. The mechanical performances of such PNCs are strongly related to the structural properties: the dispersion state of silica particles in the polymer melt is governed by the mixing protocols (e.g., solid phase mixing or solvent casting) and thermodynamics of the system (i.e., particle miscibility) which influence the filler-filler and the filler-polymer interactions.We have developed a new model nanocomposite system, equivalent to a simplified industrial one [1,2], made by solvent casting technique using colloidal silica NPs. In such model PNCs, the dispersion of colloidal silica is tuned via the surface-modification of silica particles by grafting hydrophobic molecules, i.e., silane coating agents, which promote the filler-polymer compatibility.To describe NP structure in solvents and after casting in a polymer matrix, we propose a new method which combines Small Angle X-ray Scattering (SAXS), reverse Monte Carlo (RMC) and aggregate recognition (AR) analysis [3]. This approach allows obtaining a detailed structural characterization of the silica NPs surface-modified with different silane grafting groups (i.e., tri-ethoxy, tri-methoxy or mono-methoxy silane). In particular, this analysis suggests that silane molecules with trifunctional grafting functions lead to the formation of polycondensed patches (i.e., reaction of lateral groups with neighboring molecules) on silica surface, favoring attractive interactions. On the other hand, the lowest aggregation is observed using mono-functionalized silane molecules where patches cannot form. In the near future, the SAXS-RMC-AR approach will be extended to investigate the structural properties of nanocomposite systems where silica NPs are surface-modified with silane molecules of various alkyl chain [4].[1] D. Musino, A.C. Genix, C. Fayolle, A. Papon, L. Guy, N. Meissner, R. Kozak, P. Weda, T. Bizien, T. Chaussée, and J. Oberdisse,, Macromolecules (2017)[2] G. P. Baeza, A.-C. Genix, C. Degrandcourt, L. Petitjean, J. Gummel, M. Couty, J. Oberdisse, Macromolecules (2013)[3] D. Musino, A.-C. Genix, T. Chaussée, L. Guy, N. Meissner, R. Kozak, T. Bizien, J. Oberdisse, Langmuir (2018)[4] D. Musino et al., in preparation

Using dualities of string theory, I derive modular constraints onthe generating function of MSW invariants, which coincide withgeneralized Donaldson-Thomas invariants of a Calabi-Yau threefoldat the large volume attractor point in the moduli space. Thefunction is labeled by a divisor and when the divisor isirreducible, it is known to be modular. I show that in the case ofa reducible divisor, the modularity is lost, but can be restored in a non-holomorphic completion. I find a general form of thecompletion for arbitrary degree of reducibility and provide its explicit expression up to degree 5.

Using dualities of string theory, I derive modular constraints onthe generating function of MSW invariants, which coincide withgeneralized Donaldson-Thomas invariants of a Calabi-Yau threefoldat the large volume attractor point in the moduli space. Thefunction is labeled by a divisor and when the divisor isirreducible, it is known to be modular. I show that in the case ofa reducible divisor, the modularity is lost, but can be restored in a non-holomorphic completion. I find a general form of thecompletion for arbitrary degree of reducibility and provide its explicit expression up to degree 5.