Pour tout renseignement complémentaire, veuillez contacter les
organisateurs,Hakim
Boumaza, Mathieu
Lewin
ou Stéphane
Nonnenmacher.
| 14h - 15h | Frédéric
Klopp (Sorbonne Univ.) |
The ground state of a system of interacting fermions in a random field: localization, entanglement entropy, ... Abstract: Transport in disordered solids is a phenomenon involving many actors. The motion of a single quantum particle in such a solid is described by a random Hamiltonian. Transport involves many interacting particles, usually, a small fraction of the particles present in the material. One striking phenomenon observed and proved in disordered materials is localization: disorder can prevent transport! While this is quite well understood at the level of a single particle, it is much less clear what happens in the case of many interacting particles. Physicist proposed a number of tools (exponential decay of finite particle density matrices, entanglement entropy, etc) to discriminate between transport and localization. Unfortunately, these quantities are very difficult to control mathematically for "real life" models. We'll present a toy model where one can actually get a control on various of these quantities at least for the ground state of the system. The talk is based on the PhD theses of and joint work with N. Veniaminov and V. Ognov. |
| 15h15 - 16h15 | Christof Sparber (Univ. of Illinois at Chicago) | Nonlinear bound states with prescribed angular momentum Abstract: We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schrödinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of a non-radially symmetric spatial profile which in itself is obtained via a doubly constrained energy minimization. One of the two constraints imposed is the total mass, while the other is given by the expectation value of the angular momentum around the z-axis. Our approach also allows for a new description of the set of minimizers subject to only a single mass constraint. This is joint work with I. Nenciu and X. Shen. |