On dilute quantum gases, by J.P. Solovej

Wednesday 24th Jan 2024, 11:30 am - 12:30 am. Aula: Salón de Grados
Facultad de Ciencia y Tecnología, UPV/EHU Leioa

• 1989: PhD from Princeton University.
•1991-1995: Ass. Prof., Princeton.
• From 1995: Prof. (Aarhus & Copenhagen).
• 2013-2018: ERC Advanced grant.
• 2021: Henri Poincaré prize from the IAMP
• Head of a research center for the Mathematics of Quantum Theory (QMATH)
• President of the European Mathematical Society.
• Research: Structure and stability of quantum matter from atoms to condensed matter systems.

Abstract: I will give an overview of the mathematical description of  quantum many-body systems, in particular, the ground states of gases  of many interacting identical particles. Such systems can be experimentally implemented in (very) cold atomic gases. The atoms  are either bosons (e.g. Lithium7) or fermions (e.g., Lithium6).  Bosons in three dimensions at very low temperature form  Bose-Einstein condensates (although we do not know how to show this  rigorously) and become superfluid. I will discuss recent rigorous results on the ground state energy of Bose gases in the limit  when they become dilute. I will discuss both 1,2, and 3 dimensions. The asymptotic formula for the ground state energy in 3 dimensions, the celebrated Lee-Huang-Yang formula, is in agreement with the theory of superfluidity and thus validates aspects of the theory. I will also briefly review some results about Fermi gases.  This is based on work with Agerskov, Fournais, and Reuvers.