Dynamics of Matter and Quantized Radiation

重点放在两个项目上。两者都关注量子化的低能（红外）辐射对原子和分子动力学的影响。第一个项目研究最初处于基态并受外部电磁场影响的原子和分子的行为。然后，在长度为T的时间间隔内，该外场以给定的固定方式缓慢变化；慢意味着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，系统会一直保持在它的瞬时基态附近。在非相对论性量子电动力学中，改进这一点的主要数学问题是表明基态特征向量及其能量是外场构型的平滑函数，即使基态能量嵌入在连续谱中。为了分析这一问题，对Bach、Froehlich和signal的重整化群分析进行了简化和调整。第二个项目涉及激发态原子和分子弛豫到基态的现象。在红外截止的假设下，PI和他的合作者最近对这个问题进行了全面的分析。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，只有有限的光子被发射出来。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。它的动力来自基本的数学和物理问题，来自日常现象和低能实验室实验（霓虹灯，量子化学，激光等）的物理问题。更具体地说，提出的研究有助于对基本物理现象的严格数学理解，例如“绝热极限”的存在以及受激原子和分子的基态弛豫。绝热极限的存在对于我们理解化学具有根本的重要性，因为许多理论化学都假定一种叫做玻恩-奥本海默近似的近似理论具有很高的准确性，而这种近似理论的正当性要求存在绝热极限。激发原子到基态的弛豫就是一个例子，其中开放量子系统中的能量耗散可以从第一性原理推导出来。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，这些工具可能会在其他地方得到应用。

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.