Next defenses

A quantum theory of gravitation aims at describing the gravitational interaction at every scales of energy and distance. However, understanding the emergence of our classical spacetime is still an open issue in many proposals.This thesis analyzes this problem in loop quantum gravity with tools borrowed from quantum information theory.

This is done in several steps. Since loop quantum gravity is still under construction, a pragmatic point of view is advocated and an ansazt for physical states of the gravitational field is studied at first, motivated from condensed matter physics and simple intuitions. We analyze the proposal of reconstructing geometry from correlations. Lessons on the quantum dynamics and the Hamiltonian constraint are extracted. The second aspect of this work focuses on the physics of sub-systems and especially the physics of their boundary. We begin by calculating the entanglement entropy between the interior and the exterior of the region, recovering the holographic law known from classical black hole physics. Then different boundary dynamics are studied, both in the isolated and open cases, which shed lights again on the fundamental dynamics. Finally, the last aspect of this research studies the dynamics of the boundary interacting with an environment whose degrees of freedom (gravitational or matter) forming the rest of the Universe and especially the decoherence it induces. This allows to discuss the quantum to classical transition and understand, in a given model, the pointer states of geometry.

In this thesis we take Einstein theory in dimension four seriously, and explore the special aspects of gravity in this number of dimensions. Among the many surprising features in dimension four, one of them is the possibility of `Chiral formulations of gravity' - they are surprising as they typically do not rely on a metric. Another is the existence of the Twistor correspondence. The Chiral and Twistor formulations might seem different in nature. In the first part of this thesis we demonstrate that they are in fact closely related. In particular we give a new proof for Penrose's `non-linear graviton theorem' that relies on the geometry of SU(2)-connections only (rather than on metric). In the second part of this thesis we describe partial results towards encoding the full GR in the total space of some fibre bundle over space-time. We indeed show that gravity theory in three and four dimensions can be related to theories of a completely different nature in six and seven dimension respectively. This theories, first advertised by Hitchin, are diffeomorphism invariant theories of differential three-forms. Starting with seven dimensions, we are only partially succesfull: the resulting theory is some deformed version of gravity. We however found that solutions to a particular gravity theory in four dimension have a seven dimensional interpretation as G2 holonomy manifold. On the other hand by going from six to three dimension we do recover three dimensional gravity. As a bonus, we describe new diffeomorphism invariant functionnals for differential forms in six dimension and prove that two of them are topological.

Cette thèse porte sur l’effet Lehmann, un effet hors d’équilibre couplant un gradient de température avec la rotation de la texture de gouttes cholestériques ou nématiques coexistant avec la phase isotrope.

Nous avons d’abord caractérisé les couplages thermomécaniques de Leslie, Akopyan et Zel’dovich en mesurant en phase cholestérique la vitesse de rotation des molécules dans deux configurations invariantes par translation avec des orientations différentes.

Nous avons ensuite caractérisé la texture des gouttes observées dans l’expérience de Lehmann en nous basant sur des observations optiques et des simulations numériques. Plus important, nous avons montré pour la première fois qu’il est possible d’observer l’effet Lehmann dans des gouttes nématiques achirales, à condition que la texture interne soit torsadée. Nous avons aussi utilisé un montage de photoblanchiment afin de montrer qu’il n’y a pas d’écoulements visibles au voisinage des gouttes. Ceci montre que la rotation observée est due à une rotation locale des molécules – pas à une rotation solide des gouttes.

Enfin, nous avons proposé un modèle théorique « à la Leslie » de l’effet Lehmann incluant les termes de couplage thermomécanique d’Akopyan et Zel’dovich. En appliquant ce modèle généralisé aux textures calculées numériquement, nous avons ajusté les vitesses de rotation mesurées expérimentalement et avons trouvé des valeurs pour les constantes de couplage thermomécanique bien plus grandes que celles mesurées en dessous de la transition cholestérique/isotrope. Cela montre que ce modèle est faux et que le paradigme de Leslie doit être définitivement abandonné.

TBA