Dynamics of Matter and Quantized Radiation

摘要格里斯梅尔重点介绍了两个项目。它们都涉及量子化的低能量(红外)辐射对原子和分子动力学的影响。第一个项目研究原子和分子的行为，这些原子和分子最初处于基态，并受到外部电磁场的影响。然后，在一个长度为T的时间间隔内，这个外场以静止和固定的方式慢慢改变；慢慢地，意味着T在原子或分子的时间尺度上非常大。我们的目标是理解为什么在实验中，系统会一直保持在其瞬时基态附近。在非相对论量子电动力学中证明这一点的主要数学问题是，即使基态能量嵌入在连续谱中，基态本征矢及其能量也是外场组态的光滑函数。为了分析这个问题，对Bach、Froehlich和Sigal的重整化群分析进行了简化和调整，使之适用于这个问题。第二个项目涉及到被激发原子和分子的基态弛豫现象。在红外线截止的假设下，这个问题最近被PI和他的合作者彻底分析了。现在的目标是消除红外截止的非物理假设，并表明没有红外问题发生，也就是说，只有有限多的光子被发射。这是一个致力于光(光子)与原子和分子相互作用的动力学方面的数学分析的项目。它的动机是基本的数学和物理问题，来自日常现象和低能量实验室实验(霓虹灯、量子化学、激光等)的物理问题。更具体地说，这项研究有助于从严格的数学角度理解基本的物理现象，如“绝热极限”的存在以及激发原子和分子基态的驰豫。绝热极限的存在对于我们对化学的理解是非常重要的，因为许多理论化学假设了一种称为Born-Oppenheimer近似的近似理论的良好精度，而这种近似理论的合理性要求存在绝热极限。在开放的量子系统中，能量耗散可以从第一性原理得到，激发原子基态的松弛就是一个例子。它也是产生所有可见光的主要效应之一.这个项目将加深我们对原子和分子物理学的理解，并产生新的数学工具，很可能在其他地方找到应用。

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.