The normal phase of an imbalanced Fermi gas

Recent experiments on imbalanced Fermi gases have raised interest in the physics of an impurity immersed in a Fermi sea, the so-called Fermi polaron. In this letter, a simple theory is devised to describe dilute Fermi-polaron ensembles corresponding to the normal phase of an imbalanced Fermi gas. An exact formula is obtained for the dominant interaction between polarons, expressed solely in terms of a single polaron parameter. The physics of this interaction is identified as a signature of the Pauli exclusion principle.Comment: 4 pages, 2 figures, published in PR

Ground state of a tightly bound composite dimer immersed in a Fermi Sea

In this paper we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length $a$. Working up to order $a^3$, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.Comment: 11 pages; 3 figure

Expressing Discrete Geometry using the Conformal Model

International audiencePrimitives and transformations in discrete geometry, such as lines, circles, hyperspheres, hyperplanes, have been defined with classical linear algebra in dimension 2 and 3, leading to different expressions and algorithms. This paper explores the use of the conformal algebra to express these discrete primitives in arbitrary dimensions with a minimum of expressions and then algorithms. Starting with hyperspheres and hyperplanes, a generalization to $k$-sphere is then proposed. This gives one simple and compact formula, valid for all geometric conformal elements in R^n, from the circle to the hypersphere, and the line to the hyperplane

Cartes de photons et visibilité

Les méthodes de simulation d'éclairage par tracé de photons sont souvent utilisées pour leur simplicité et leur versatilité. Les deux étapes classiques de ces approches sont : (i) les calculs d'inter-réflexions lumineuses, indépendantes du point de vue, correspondant à des suivis de chemins lumineux dont les impacts sur les surfaces de la scène sont stockés sous forme de cartes de photons ; (ii) l'exploitation des cartes de photons pour produire une ou plusieurs images de l'environnement virtuel. La première phase repose exclusivement sur des méthodes de Monte-Carlo ; la seconde requiert au moins une estimation de densité pour le calcul d'éclairement. Malheureusement, le tracé de photons est également connu pour les différents biais produits lors de l'estimation de densité des photons pour le calcul de l'éclairement en un point. Ce rapport montre pourquoi la visibilité est un élément fondamental lors de l'estimation de densité ; nous proposons de la prendre en compte de manière précise pour réduire ou supprimer certains biais. Nos résultats mettent en évidence l'importance de la visibilité dans la qualité des images produites

Lazy visibility evaluation for exact soft shadows

Présentation invitée de l'article du même nom publié en 2012 dans la revue Computer Graphics Forum.International audienceThis paper presents a novel approach to compute high quality and noise-free soft shadows using exact visibility computations. This work relies on a theoretical framework allowing to group lines according to the geometry they intersect. From this study, we derive a new algorithm encoding lazily the visibility from a polygon. Contrary to previous works on from-polygon visibility, our approach is very robust and straightforward to implement. We apply this algorithm to solve exactly and efficiently the visibility of an area light source from any point in a scene. As a consequence, results are not sensitive to noise, contrary to soft shadows methods based on area light source sampling. We demonstrate the reliability of our approach on different scenes and configurations

A Framework for n-dimension Visibility Calculation

4 pagesVisibility computation is a fundamental task in computer graphics, as in many other scientific domains. While it is well understood in two dimensions, this does not remain true in high dimensional spaces. Using Grassmann Algebra, we propose a framework for solving visibility problems in any n-dimensional spaces, for n ≥ 2. Our presentation recalls the problem statement, in two and three dimensions. Then, we formalize the space of n-dimensional lines. Finally, we show how this leads to a global framework for visibility computations, giving an example of use with exact soft shadows

Lazy visibility evaluation for exact soft shadows

International audienceThis report presents a novel approach to compute high quality and alias-free soft shadows using exact visibility computations. This work relies on a theoritical framework allowing to group lines according to the geometry they intersect. From this study, we derive a new algorithm encoding lazily the visibility from a polygon. Contrary to previous works on from-polygon visibility, our approach is very robust and straightforward to implement. We apply this algorithm to solve exactly and efficiently the visibility of an area light source from any point in a scene. As a consequence, results are not sensitive to noise, contrary to soft shadows methods based on area light source sampling. We demonstrate the reliability of our approach on different scenes and configurations

Ultra-cold Polarized Fermi Gases

Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing experimentally fermionic superfluids with imbalanced spin populations. We discuss how these developments have shed a new light on a half- century old open problem in condensed matter physics, and raised new interrogations of their own.Comment: 27 pages; 8 figures; Published in Report in Rep. Prog. Phys. 73 112401 (2010