LAUSR

In this work, we investigate the mean-field limit of a model consisting in m > 1 tracer particles, coupled to an interacting boson field. We assume the mass of the tracer particles and the expected number of bosons to be of the same order of magnitude N > 1 and we investigate the N Ñ 8 limit. In particular, we show that the limiting system can be effectively described by a pair of variables pXt, φtq P R 3m ˆ HpRq that solve a mean-field equation. Our methods are based on proving estimates for the number of bosonic particles in a suitable fluctuation state ΩN,t. The main diffculty of the problem comes from the fact that the interaction with the tracer particles can create or destroy bosons for states close to the vacuum.