Seminarium KMMF "Teoria Dwoistości"

I will discuss some recent mathematical results on themacroscopic behavior of large quantum systems of weakly-interacting bosonsin low-energy regime. A crucial property of bosons is that they canundergo the Bose-Einstein condensation, in which a large fraction ofparticles can occupy a common quantum state. In the first part of thetalk, I will explain how to justify the Bose-Einstein condensation and theeffective, nonlinear, one-body theory for the condensation from thelinear, many-body, Schrodinger theory. In the second part of the talk, Iwill discuss the next order correction given by Bogoliubov's theory, inwhich the fluctuations around the condensation are described by aneffective, quadratic Hamiltonian acting on Fock space.