Compact packings of spheres

Thomas Fernique (LIPN, CNRS et U. Paris 13)

It is well known that the best way to pack oranges in a (very large) box is to place them on a face-centered cubic lattice (also known as checkerboard), although this has been formally demonstrated only in 1998 (with difficulty). This talk focuses on what happens when the dimension or number of different spheres change. In particular, so-called compact packings (the term will be defined properly) seem good candidates to maximize density. In this tallk, we propose : a) a non-technical survey of the known mathematical results ; b) an overview of the underlying computer problems (interval arithmetic, resolution of systems of polynomial equations, combinatorial exploration) ; (c) a discussion of possible applications in chemistry, including self-assembly of supercrystals ; d) a discussion of numerical simulations that may be of interest in this context.

Quantum spin liquids: an experimental view

Fabrice Bert (LPS Orsay)

Spin liquids are fascinating states of matter where quantum fluctuations are strong enough to prevent any kind of magnetic ordering down to absolute zero temperature. Spin liquid physics has been for long a rich playground for theoreticians to discover novel quantum states and concepts, often relevant to other fields such as high Tc superconductivity, and there are now several materials realizing such ground states. I will present an experimental investigation with resonance techniques of two of them: a vanadium oxyfluoride compound where the V4+ ions form a unique S = ½ breathing kagome lattice which consists of alternating equilateral triangles, preserving the full frustration of the isotropic model, and the recently discovered Y-kapellasite which realizes an original spatially anisotropic kagome model.

Continuous-time Quantum Walks

Kirone Mallick (IPhT CEA Saclay)

Quantum analogs of classical random walks have been defined in quantum information theory as a useful concept to implement  algorithms. Due to  interference effects, statistical properties of quantum walks can drastically differ from their classical counterparts, leading to much faster computations.
In this talk, we  shall discuss  various  statistical properties of continuous-time quantum walks on a  lattice, such as: survival properties of quantum  particles in the presence of traps (i.e. a quantum generalization of the Donsker-Varadhan stretched exponential law), the growth of a quantum  population in the presence of a  source, quantum return probabilities and  Loschmidt echoes.

Introduction de propriétés topologiques dans un métamatériau

Fabrice Lemoult (Institut Langevin, ESPCI, Paris)

Les métamatériaux sont des milieux artificiels qui offrent des propriétés de propagation exotiques, comme par exemple des effets de réfraction négative. Ces effets sont la conséquence de l’interaction des ondes avec la cellule unité composant ces métamatériaux, celle-ci étant beaucoup plus petite que la longueur d'onde de travail. Dans le domaine des micro-ondes, un exemple de cellule unité est une simple tige métallique placée sur un plan de masse, et dans le cas de l’acoustique une simple canette de soda jouant le rôle de résonateur de Helmholtz. Dans un milieu composé de nombreuses cellules unités, la propagation de l'onde est décrite simplement avec le modèle du polariton, c'est-à-dire par une relation de dispersion résultant de l'hybridation de l'onde et de la résonance individuelle de chaque résonateur. Dans cet exposé, nous montrerons comment aller au-delà de cette description habituelle permet d’introduire des propriétés topologiques à la propagation des ondes.