Pour tout renseignement complémentaire, veuillez contacter les
organisateurs, Hakim
Boumaza, Mathieu
Lewin
ou Stéphane
Nonnenmacher.
| 14h - 15h |
Alvise Bastianello (CNRS & Paris-Dauphine) |
Soliton gases in integrable PDEs from quantum integrability.
Abstract: Understanding the thermodynamics and hydrodynamics of classical nonlinear waves remains a challenging problem, even in integrable partial differential equations (PDEs) where exact solutions exist. The soliton gas framework offers a heuristic approach by treating solitons as extended, but otherwise non-interacting, particles. While appealing, this approach has been known to fail in several important cases, remaining an open challenge since the 1990s. In this talk, I will examine the limitations of the conventional soliton gas approach, and use semiclassical limits of quantum integrability as an alternative path to the exact thermodynamics of classical integrable partial differential equations. |
| 15h15 - 16h15 | Jared Wunsch (Northwestern) |
Gutzwiller trace formula for singular potentials.
Abstract: The Gutzwiller trace formula relates the asymptotic spacing of quantum-mechanical energy levels in the semiclassical limit to the dynamics of periodic classical particle trajectories. We generalize this result to the case of non-smooth potentials, for which there is partial reflection of energy from derivative discontinuities of the potential. It is the periodic trajectories of an associated branching dynamics that contribute to the trace asymptotics in this more general setting; we obtain a precise description of their contribution. This is joint work with Mengxuan Yang and Joey Zou. |