Pour tout renseignement complémentaire, veuillez contacter les
organisateurs, Hakim
Boumaza, Mathieu
Lewin
ou Stéphane
Nonnenmacher.
| 14h - 15h | Gabriel Rivière (Nantes) |
Nonlinear chaotic Vlasov equations.
Abstract: I will present a joint work with Yann Chaubet and Daniel Han-Kwan (Nantes). I will discuss the long time behaviour of the nonlinear Vlasov equation set on a negatively curved manifold when the interaction kernel is smooth. I will explain that, for small initial data supported away from the zero section, solutions to this equation converge exponentially fast to an equilibrium state of the linear problem. The proof of this result relies on tools from microlocal analysis initially developed in the context of hyperbolic dynamical systems. |
| 15h15 - 16h15 |
Eric Cancès (ENPC) |
Quantum Hamiltonians for twisted bilayer graphene: construction and spectral properties
Abstract: The engineering of multilayer two-dimensional and moiré materials with tailored electronic, optical, and mechanical properties has become a central theme in contemporary condensed matter physics and materials science. In this talk, I will discuss the construction and spectral analysis of quantum Hamiltonians modeling the electronic structure of one of the most prominent moiré materials: twisted bilayer graphene. In the periodic setting (untwisted bilayer graphene and twisted bilayer graphene with a rational twist parameter), first-principles Density Functional Theory models yield mean-field Hamiltonians whose spectral properties can be described in detail using Bloch theory. In the aperiodic case (irrational twist parameter), one can still build approximate mean-field Hamiltonians and study their spectra by either embedding the problem into a higher dimensional periodic framework or by using the |