Granular materials can be defined as large assemblies of macroscopic particles (i.e. the grains). When external energy is applied to these systems, they can reach a non-equilibrium steady state (NESS), where the statistical properties of the dynamics remain constant, but the time reversal symmetry is broken by forcing and dissipative mechanisms. The main idea of my talk will be to show how granular materials subjected to mechanical vibration can realise NESSs where equilibrium-like and nonequilibrium phenomena are deeply intertwined. First, I will report on our experimental study of the self-assembly processes of binary mixtures of grains vibrated on a substrate. Starting from a disordered configuration, and depending on the size ratio and number proportions of the two grain species, we observed the spontaneous self-assembly of quasi-crystalline structures [1] and periodic square crystals [2]. Remarkably, this follows predictions from the equilibrium phase diagram of a hard disk model following conservative dynamics. We have also obtained experimental conditions that realise a stable coexistence between the square crystal phase and a granular amorphous fluid. Using numerical simulations, we showed that the observed phenomenology resembles that of a first-order equilibrium phase transition, but with the two phases coexisting at different effective temperatures, which is a striking nonequilibrium effect. Unexpectedly, the denser crystalline phase is hotter than the less dense liquid phase. Through qualitative arguments and supported by kinetic theory, we elucidate the role of the coupling between local structure and energy transfer mechanisms in maintaining kinetic temperature gradients across the fluid-crystalline interface. In the last part of my talk I will discuss how, by changing the external driving parameters and considering dilute monodisperse systems, our setup can also be used as a playground for the study of absorbing phase transitions and hyperuniform fluids. I will summarise theoretical and numerical results [3,4] and present some preliminary experimental attempts. [1]: A. Plati, R. Maire, E. Fayen, F. Boulogne, F. Restagno, F. Smallenburg, and G. Foffi, Nat. Phys. 20, 465–471 (2024) [2]: Self-assembly and non-equilibrium phase coexistence in a binary granular mixture arXiv:24LF.21576 [3]: R. Maire, A. Plati, M. Stockinger, E. Trizac, F. Smallenburg, G. Foffi, Phys. Rev. Lett. CR2, 238202 (2024) [4]: R. Maire, A. Plati, J. Chem. Phys. 161, 054902 (2024)

Upon approaching a magnet, any nonmagnetic material feels a force. This force finds its origin in the spin and charge (orbital) motions of the electrons of the materials under the influence of the magnet field. For most materials this force is attractive because it is dominated by the spin magnetic susceptibility which is always paramagnetic. When the force appears repulsive the material is said to be diamagnetic and its magnetic response is then determined by the orbital motion of electrons. A well known example of diamagnetic material is water. In this talk I will review the microscopic theory of "diamagnetism" encoded by the orbital magnetic susceptibility of electrons in metals and insulators. First, I will remind why orbital magnetism is a genuine quantum effect related to the quantum motion of a charge in magnetic field. I will then show how the early theory of Landau and Peierls succeeds in describing the orbital response of single band metals but fail in describing multiband systems. Then I will present our work highlighting the key role of interband effects encoded in the quantum geometry of Bloch states (Berry curvature and quantum metric) in order to correctly describe the orbital magnetic susceptibility of multiband systems metal and insulators.

Cette soutenance résumera mes recherches menées en optique, en électromagnétisme et en optique quantique. L’idée générale est le développement une théorie décrivant les propriétés optiques de matériaux, composites à l’échelle macroscopique et baptisés "métamatériaux", enrichis en structures quantiques ( par ex. boites quantiques ou des défauts ponctuels luminescents). Le but final de ces investigations est l’obtention d’équations effectives pour décrire le comportement global de ces systèmes. Nous porterons une attention particulière à la notion "d'indépendance avec le choix de la jauge" des résultats finaux. Cette soutenance se terminera avec une ouverture sur l'apport de ces théories effectives pour décrire le comportement d'une catégorie de réseaux de neurones baptisée "calcul par réservoir".