Mini Curso: On Bose-Einstein Condensation for interacting particles (II)

Minicurso de tres días lunes 21, miércoles 23 y viernes 25 de octubre. 

Abstract: To prove Bose-Einstein Condensation (BEC) for a system of interacting quantum mechanical particles is an important challenge for mathematical physics. So far the only result in the thermodynamic limit is the famous paper by Kennedy, Lieb and Shastry that establishes condensation for a particular system of bosons on a lattice, interacting via a hard core potential and at exactly half-filling. The result in this setting depends essentially on a special symmetry satisfied by the system, namely reflection positivity.

For continuous systems, there has in recent years been much progress on understanding the energy of the interacting Bose gas at low density. Even very precise energy bounds will not imply BEC in the thermodynamic limit. However, on finite length scales, there is an intimate connection between these bounds and BEC.In this mini-course, I will discuss the mathematics of BEC and review the proofs of the results mentioned above.