Universal Description of the Bose Gases

In UniBoGas my aim is to prove universal expansion formulas for the low energy levels of the dilute Bose gases, showing their dependence on just one parameter, namely the scattering length of the potentials between the particles.

I am going to work out to which order of precision of the expansion the universal description still holds, and for which kind of systems.

The classification of the systems that satisfy the universality is obtained through studying the expansions in three directions by paradigmatic examples: I am going to evaluate the energy for systems with potentials with repulsive and attractive parts, I am going to approximate the energy of systems composed by two kinds of bosons by the energy of effective non-linear models and I am going to evaluate the low energy levels of the hard-spheres (hard-core potential) system.The methodology used includes both the improvement of pre-existing techniques in the Bogolubov Theory and the introduction of new methods of localization, Semi-Classical Analysis and variational methods.Other than on Mathematical Physics, the results of UniBoGas will have an impact also on disciplines like Functional Analysis, Experimental Physics and Quantum Chemistry for the Bose gases and will contribute to further understand the phenomenon of Bose Einstein Condensation.