Dynamics of Matter and Quantized Radiation

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AbstractGriesemerThe focus is on two projects. Both of them concern the effectof quantized low-energy (infrared) radiation on the dynamics ofatoms and molecules. The first project studies the behavior ofatoms and molecules that are initially in their ground state andsubject to an external electromagnetic field. Then, in a timeinterval of length T this external field is slowly changed in agiven and fixed manner; slowly meaning that T is very large on thetime scale of the atom or molecule. The goal is to understand why,in an experiment, the system would stay close to its instantaneousground state at all times. The main mathematical problem inproving this within non-relativistic quantum electrodynamics is toshow that the ground state eigenvector and its energy are smoothfunctions of the external field configuration, even though theground state energy is embedded in the continuous spectrum. Toanalyze this problem the renormalization group analysis of Bach,Froehlich, and Sigal is simplified and adjusted to the problem athand. The second project concerns the phenomenon of relaxation tothe ground state of excited atoms and molecules. Under theassumption of an infrared cutoff this problem has recently beencompletely analyzed by the PI and his collaborators. The goal nowis to remove the un-physical assumption of an IR cutoff and toshow that no infrared problem occurs, that is, that only finitelymany photons are emitted.This is a project devoted to the mathematical analysis ofdynamical aspects of light (photons) interacting with atoms andmolecules. It is motivated by fundamental mathematical andphysical problems, the physics problems stemming from every dayphenomena and from low energy laboratory experiments (neon lamp,quantum chemistry, laser light etc). More specifically, theproposed research contributes to a rigorous mathematicalunderstanding of basic physical phenomena, such as the existenceof ''adiabatic limits'' and the relaxation to the ground state ofexcited atoms and molecules. The existence of adiabatic limits isof fundamental importance for our understanding of chemistry,since much of theoretical chemistry assumes good accuracy of anapproximative theory, called Born-Oppenheimer approximation, whosejustification requires existence an adiabatic limit. Therelaxation to the ground state of an excited atom is an examplewhere dissipation of energy in an open quantum system can bederived from first principles. It is also one of the main effectsresponsible for the production of all visible light. This projectwill deepen our understanding of the physics of atoms andmolecules and produce new mathematical tools that will likely findapplications elsewhere.