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Marco Falconi

External Potentials Generated by the Interaction with a Semiclassical Field

Abstract: In physical experiments of condensed matter, quantum particles (atoms) are immersed in controllable external potentials, such as harmonic traps and optical lattices. These potentials are obtained using finely tuned lasers, or magnetic fields, acting on the atoms. In this talk I will present some results, obtained in collaboration with Michele Correggi, that shed light on the procedure above. We consider a coupled system consisting of N quantum particles in (linear) interaction with a scalar boson field. Using tools of infinite dimensional semiclassical analysis, a partially classical limit on the scalar field is studied. We prove the convergence of the partial trace of the full Hamiltonian to an effective reduced Hamiltonian on the particles alone (in either norm or strong resolvent sense). We also prove the convergence of the ground state energy of the full quantum system to the infimum on all possible classical field configurations of the ground state energy of the effective Hamiltonian.