Bogoliubov-De Gennes normal-modes analysis of a cylindrically symmetric Bose-Einstein condensate

This thesis analyzes the collective modes of a Bose-Einstein condensate trapped in a harmonic cylindrically symmetric potential well. We use the Gross-Pitaeskii equation to evaluate the mean-field ground state, and the Bogoliubov-De Gennes formalism to compute normal modes. We solve both problems numerically by means of a newly developed code based on standard numerical techniques. In particular, we devised a selfconsistent Newton-Raphson algorithm for the ground-state computation and we used LAPACK libraries to solve the normal-mode problem. We discuss the agreement of our numerical calculation with recent experiments of an atomic BEC confined in a electromagnetic trap. Advisor: Dr. Nicola Manini Co-Advisor: Dr. Luca Salasnich