Research Interests


Gender and physics

The small proportion of female students and researchers in physics and computer sciences is a serious problem for a modern egalitarian society. This problem can be cured, as shown by the Carnegie Mellon School of Computer Science, where the proportion of female students went from 7% to 50%. After being a gender equality officer at the faculty of science and engineering of Sorbonne University, I am now collaborating with two sociologists (Beate Collet and Elise Verley) and a PhD student (Jeanne Goulpier) to analyze the situation at Sorbonne University and set up solutions.

Geometric methods in solid-state physics

The tools of differential geometry proved very powerful to solve some long-standing problems, such as the correct definition of electric and orbital polarization or the understanding of the quantum Hall effect. They allowed us to prove that exponentially localized Wannier functions can be constructed. They also play a prominent role in the discovery of new phenomena, such as Chern insulators. These concepts, which are new in solid-state physics but venerable in mathematics, go by the name of Berry phase, Berry connection, connection on fibre bundles, triviality of bundles, Chern numbers and de Rham theorem. This is an exciting field where the unifying picture offered by differential geometry is very precious.

Quantum fields and quantum groups

 Many-body theory and quantum field theory express physical properties as infinite sums of Feynman diagrams. These diagrams give a clear picture of the physical phenomena but they have poor algebraic properties. It turns out that quantum groups provide a powerful algebraic tool for quantum field calculations. Wick's theorem is the twisted product of quantum groups, the expectation value over the vacuum is the counit, quantum states are positive 1-cochains, etc. In fact the quantum group language is a natural framework for bosons and fermion fields, normal products, operator and time-ordered products, renormalisation. Moreover, the quantum group concepts are still valid beyond the usual quantum field framework. For instance, it is possible to consider noncommutative normal products and time-ordered products. Quantum groups can provide an efficient framework to calculate the Green functions of degenerate systems.

Quantum fields in curved spacetimes

  Quantum fields in curved spacetimes have made tremendous progress through the efforts of Brunetti, Fredenhagen, Hollands, Wald, Dutsch, Rejzner and coll. culminating with a background independent formulation of the quantum field theory of gravitation. Some of these works make heavy use of locally convex topological vector spaces and convex bornological spaces. There are many excellent textbooks on locally convex spaces but the results of bornology theory are often quit difficult to locate. I have scanned some of these texts: PUSH!Bornological library 

The colour of minerals

Colour is one of the most obvious properties of minerals and gemstones but the origin of colour is often quite difficult to determine. For instance, it is only recently that we know why fossil ivory of mastodons (13 million years old) turns blue when heated, so blue that it was used as a substitute for turquoise in the Middle Age. The colour of ruby and emerald is due to the presence of chromium impurities surrounded by a distorted octahedron of oxygen. But the reason why ruby is red and emerald is green is not clear. Two theoretical models are used to calculated the colour of minerals and gems, (i) Green function and (ii) effective Hamiltonian:
(i) Recently, the colour of semiconductors was calculated successfully using Green function methods such as the GW approximation and the Bethe-Salpeter equation. These methods assume that the initial state (before interaction) is degenerate.
(ii) The colour of transition metals and rare-earth compounds cannot be calculated ab initio but the position of the bands in optical absorption spectra can be computed by diagonalizing an effective Hamiltonian depending on parameters. In this method, the initial state is degenerate but the values of the parameters must be fitted.
To unify both approaches, we have to set up a Green function method using degenerate initial states.

Light and biological cells

Light and biological cells have a number of fascinating interactions. Many animals, mushrooms and bacteria are bioluminescent. Photosynthesis is also an obvious and vital case of interaction between light and plant cells. Only a few species are bioluminescent. However, all living organisms spontaneously emit a very weak light know as "autoluminescence" or "ultraweak photon emission" (UPE). This light is in the visible range and is not due to black body radiation. Autoluminescence is due to the fact that among the many biochemical reactions that take place in the cell, some of them are chemiluminescent (they create excited species that relax radiatively to their ground states). The most prominent luminescent excited species are thought to be singlet oxygen and triplet carbonyl. Texte remplaçant l'image
Pelargonium leaf (K. Creath, A look at some systemic properties of self-bioluminescence. In The Nature of Light: Light in Nature II, SPIE Proceedings 7057 (2008) 705708)

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Autoluminescence of a human hand (A. Rastogi and P. Pospisil, Spontaneous ultraweak photon emission imaging of oxidative metabolic processes in human skin: effect of molecular oxygen and antioxidant defense system, J. Biomed. Opt., 16 (2011) 096005)

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Autoluminescence of a human torso (R. van Wijk, M. Kobayashi and E. P. A. van Wijk, Anatomic characterization of human ultra-weak photon emission with a moveable photomultiplier and CCD imaging, J. Photochem. Photobiol. B, 83 (2006) 69-76

Time-reversal symmetry, parity and x-ray absorption

The absorption of x-rays by matter is mainly due to electric dipole transitions but electric quadrupole transitions can also be observed. Pure electric dipole and quadrupole transitions are even under parity, in other words, they do not distinguish between two samples that are related by an inversion.  José Goulon realized that the interference between electric dipole and quadrupole transitions provides a parity-odd transition operator, with which properties of chiral materials can be investigated. On the other hand, time-reversal symmetry divides the materials into two classes, those that are symmetric and those that are not symmetric. The charge is a time-reversal symmetric but the spin and the current are reversed by time-reversal. Thus time-reversal odd spectroscopies enable us to measure properties of the electronic current and spin in materials. By using the possible combinations of time-reversal, parity and rotation symmetries, three new x-ray spectroscopies were discovered: natural circular dichroism (parity odd, time-reversal even, rank 2), magnetochiral dichroism (parity odd, time-reversal odd, rank 1) and nonreciprocal linear dichroism (time-reversal odd, rank 2 and 3). As a possible application, these new spectroscopies give unique information on the magnetic symmetry group of chiral and magnetoelectric materials.


Drawing a realistic rainbow is not so easy. Two great rainbow drawers are Raymond Lee  and  Philip Laven. We developed a theory describing the scattering of a partially coherent beam of light by a dielectric sphere. When this theory is applied to the scattering of sunlight by a raindrop, we obtain the following rainbow slices: for raindrop size of 0.1 to 0.5 mm  pdf , for raindrop size of 0.6 to 1 mm  pdf . If the sun were a coherent source of light the rainbows would look like this: for raindrop size of 0.1 to 0.5 mm  pdf, for raindrop size of 0.6 to 1 mm  pdf. References: R.L. Lee, Mie theory, Airy theory, and the natural rainbow, Appl. Opt. 37 (1998) 1506-19; P. Laven, Simulation of rainbows, coronas, and glories by use of Mie theory, Appl. Opt. 42 (2003) 436-444; D. Cabaret, S. Rossano, Ch. Brouder, Mie scattering of a partially coherent beam, Opt. Commun. 150 (1998) p.239-50.