Bose Particles in a Box: Convergent Expansion of the Ground State in the Mean Field Limiting Regime

40th LQP Workshop "Foundations and Constructive Aspects of QFT"
Alessandro Pizzo on June 23, 2017

I shall report on a novel multi-scale technique to study many-body quantum systems. The method is based on the Feshbach-Schur map and the scales are represented by occupation numbers of particle states. Consider an interacting Bose gas at zero temperature, constrained to a finite box and in the mean field limiting regime, where the N gas particles interact through a pair potential of positive type and with an ultraviolet cut-off. The (nonzero) Fourier components of the potential are assumed to be sufficiently large with respect to the corresponding kinetic energies of the modes. For this system, we provide a convergent expansion of the ground state of the Hamiltonian in terms of the bare operators. In the limit Nā†’āˆž the expansion is up to any desired accuracy.