Many-Body Quantum Physics
The Mathematical Physics of Cold Quantum Gases
Since the first experimental realization of Bose-Einstein condensation (BEC) in trapped, dilute alkali gases in 1995 the physics of ultracold quantum gases has become a large research field worldwide, both experimentally and theoretically. This is at present also a main research topic in the Mathematical Physics Group.
Basic results, both on dilute, trapped quantum gases and on denser gases in optical lattices, have been obtained in various collaborations involving in particular E. H. Lieb (Princeton University), R. Seiringer (on leave, presently at Princeton University) and J.P. Solovej (Copenhagen University). These include mathematically rigorous derivations of the ground state energy and density of dilute, trapped Bose gases, dimensional reduction in elongated or disc-shaped traps and quantum phase transitions and BEC in optical lattices.
The research up to 2006 is summarized in the monograph The Mathematics of the Bose Gas and its Condensation, available on the website arXiv:cond-mat/0610117. In the past two years the main focus has been on rotating Bose gases and quantized vortices in collaborations between Jean-Bernard Bru, Michele Correggi (Pisa), Peter Pickl (Munich), Tanja Rindler-Daller (Cologne) and Jakob Yngvason.
Physics of many particles, Statistical physics, Thermodynamics
The difficulty to describe a system in detail increases with the number of particles. Statistical descriptions however become more and more precise if the number of particles is increasing. In the thermodynamic limit few properties like energy, volume and entropy suffice to fix the state of the system. Thermodynamics searches for relations between these few properties, statistical physics tries to control the thermodynamic limit and to evaluate these properties. For heavy atoms with many electrons in external fields one can choose several different limiting conditions revealing different aspects.
Both in statistical physics and in quantum field theory we deal with systems having infinitely many degrees of freedom. Therefore the two research areas are closely related.