|DATE||February 12 (Tue), 2019|
|TITLE||Semiclassical limit of solitons between Hartree systems and Vlasov-Poisson systems|
Statistical dynamics of a system of collisionless particles in the gravitational field they generate is described by a Vlasov-Poisson system. By quantizing it, we get a Hartree system which describes statistical dynamics of a system of bosons. It has been an one of central problems of mathematical physics to rigorously prove the convergence of the semiclassical limit between IVP from Hatree systems to Vlasov-Poisson systems. In this talk, we turn to semiclassical limits of solitons between them. We will see that the semiclassical problems for solitons are independent of problems for IVP so completely different approaches, for example, variational approaches are required to prove it.