Bose particles in a box: A convergent expansion of the ground in the mean field limiting regime

by A. Dal Pizzo

Friday 30 Sept 2016, 11:00 → 13:00 Europe/Rome

Aula Majorana (Dipartimento di Fisica - Ed. G.Marconi)

I shall report on a novel multi-scale technique to study many-body quantum systems where the total number of particles is kept fixed. The method is based on Feshbach-Schur map and the scales are represented by occupation numbers of particle states. First, I consider a three-modes (including the zero mode) Bogoliubov Hamiltonian for a sufficiently small ratio between the kinetic energy and the Fourier component of the (positive type) potential corresponding to the two nonzero modes. For any space dimension d d\geq 1 and in the mean field limiting regime (i.e., at fixed box volume |\Lambda| and for a number of particles, N, sufficiently large) this method provides the construction of the ground state and its expansion in terms of the bare operators that in the limit N \to \infty is up to any desired precision. In space dimension d\geq 3 the method provides similar results for an arbitrarily large (finite) box and a large but fixed particle density \rho;, i.e., \rho is independent of the size of the box. Then, I'll show how this method can be extended to finitely many modes (i.e., particles in a finite box, and u.v. cut-off imposed on the two-body potential) interacting according to the complete Hamiltonian in the mean field limiting regime.