Alessandro Olgiati

Multi-component condensates, or mixtures of condensates, consist of two or more distinct populations of identical bosons which occupy the same one-body state.
In a recent joint work with Alessandro Michelangeli and Phan Thành Nam, we proved that, for mixtures in the Gross-Pitaevskii limit, at the leading order in the number of particles, the ground state energy is given by the minimum of a suitable effective functional. We also studied the time-dependent behavior, and proved that the effective dynamics of such systems is ruled by coupled non-linear Schrödinger equations, one for each component of the condensate.
I will devote the initial part of the talk to introducing the mathematical framework of condensation with scaling limits. Then, prior to stating our results, I will also recall some important theorems concerning the ground state and time-dependent properties of single-component bosonic systems.