Abstract:
I will present problems of my active interest, which reflect recent progress and open challenges in the asymptotics of quantum fields. Such fields characterize highly non-classical settings of particle dynamics. One problem addresses the passage from microscopic to macroscopic non-relativistic dynamics of quantum dilute gases (``Bose-Einstein condensates'') by accounting for corrections to a known mean field limit (nonlinear Schroedinger equation). Another problem will touch upon the role of scattering in quantum information and computing. If I have time, I will discuss a third problem, namely, the high-energy, relativistic behavior of the Yang-Mills quantum field theory, which is relevant to determining scattering cross sections in collisions of subatomic particles. |