Dynamics of Matter and Quantized Radiation

University Of Alabama At Birmingham, Birmingham AL

Investigators

Abstract

Abstract Griesemer The focus is on two projects. Both of them concern the effect of quantized low-energy (infrared) radiation on the dynamics of atoms and molecules. The first project studies the behavior of atoms and molecules that are initially in their ground state and subject to an external electromagnetic field. Then, in a time interval of length T this external field is slowly changed in a given and fixed manner; slowly meaning that T is very large on the time scale of the atom or molecule. The goal is to understand why, in an experiment, the system would stay close to its instantaneous ground state at all times. The main mathematical problem in proving this within non-relativistic quantum electrodynamics is to show that the ground state eigenvector and its energy are smooth functions of the external field configuration, even though the ground state energy is embedded in the continuous spectrum. To analyze this problem the renormalization group analysis of Bach, Froehlich, and Sigal is simplified and adjusted to the problem at hand. The second project concerns the phenomenon of relaxation to the ground state of excited atoms and molecules. Under the assumption of an infrared cutoff this problem has recently been completely analyzed by the PI and his collaborators. The goal now is to remove the un-physical assumption of an IR cutoff and to show that no infrared problem occurs, that is, that only finitely many photons are emitted. This is a project devoted to the mathematical analysis of dynamical aspects of light (photons) interacting with atoms and molecules. It is motivated by fundamental mathematical and physical problems, the physics problems stemming from every day phenomena and from low energy laboratory experiments (neon lamp, quantum chemistry, laser light etc). More specifically, the proposed research contributes to a rigorous mathematical understanding of basic physical phenomena, such as the existence of ''adiabatic limits'' and the relaxation to the ground state of excited atoms and molecules. The existence of adiabatic limits is of fundamental importance for our understanding of chemistry, since much of theoretical chemistry assumes good accuracy of an approximative theory, called Born-Oppenheimer approximation, whose justification requires existence an adiabatic limit. The relaxation to the ground state of an excited atom is an example where dissipation of energy in an open quantum system can be derived from first principles. It is also one of the main effects responsible for the production of all visible light. This project will deepen our understanding of the physics of atoms and molecules and produce new mathematical tools that will likely find applications elsewhere.