Sep 20, 2018 3:45 pm - Nielsen Hall 170 - Colloquium
Alexander Turbiner - UNAM - Mexico City
Quantum (classical) many-body problem: recent advances

Many body problem plays a central role in many physics sciences including celestial mechanics, atomic-molecular physics, nuclear physics. Its main characteristics is that the potential depends on relative distances between bodies alone. It is one of the most difficult problems in theoretical physics for more-then-two-body case. Recently, a new concept was pronounced: we will study solutions of n-body problem which depend on relative distances ALONE. In this case n-body problem becomes equivalent to quantum (classical) top in constant magnetic field or to multi-dimensional particle moving in curved space with remarkable metric. Since the ground state function - the main object in quantum mechanics - and choreographies in classical mechanics (in Newtonian gravity) are functions of relative distances ONLY they can be treated in much simpler way then up to now. The example of Helium and Lithium atoms will be given. n-body harmonic oscillator and n-body rational Calogero model will be briefly discussed. Animations of choreographies in Newtonian gravity will be demonstrated.