Quantum-Mechanical Matter Interacting with the Quantized Radiation Field

量子力学物质与量子化辐射场相互作用

• 批准号: 0100160
• 负责人: Marcel Griesemer
• 金额: $ 6.4万
• 依托单位: University of Alabama at Birmingham
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100160&HistoricalAwards=false
• 关键词: Quantum; Mechanical; Matter; Interacting; Quantized

Within the standard model of non-relativistic quantum mechanical matter interacting with the quantized radiation field methods are developed to show that an isolated atom or molecule prepared in a, possibly highly exited, bound state is unstable and eventually relaxes to its ground state by emitting photons. Similarly, the exited states of a free charged particle are not stable. It is shown that photons which are not bound to the electron escape ballisticly while the particle relaxes to a state of minimal energy followed by a cloud of soft photons (dressed one-electron state) in which it propagates according to a reduced dynamics. The key problem in the case of an atom is to show that no infrared problem occurs. For a free charged particle an infrared problem does occure and one has to deal with nonequivalent representations of the CCR. - The proofs require as an ingredient good control over the spectral properties of the Hamilton operator and, in addition, asymptotic completeness of Rayleigh scattering and Compton scattering of the respective system. These prerequisites are established by methods and techniques inspired by similar methods and techniques in the spectral and scattering theory of $N$-particle Schr\"odinger operators, such as Mourre theory, propagationestimates, the construction of suitable propagation observables and others. In addition ideas and methods from constructivequantum field theory (soft photon bounds, Rosen estimates, renormalization group analysis) are employed.This research leads to a mathematically rigorous understanding of physical phenomena such as the radiative decay of atoms, the photo effect, and Compton scattering. These are phenomena which are at the heart of many technical devices and which determine our visual impression of the world. Furthermore the phenomenon of radiative decay (or the relaxation to the ground state) and the similar phenomenon of return to equilibrium at positive temperature play key roles in attempts to understand dissipative, irreversible behavior in the quantum theory of open systems. The mathematical methods which are developed apply equally to other physical systems such a particle in a crystal interacting with quantized lattice vibrations (phonons), and find currently application in the study of return to equilibrium of matter interacting with radiation at positive temperature.

在非相对论量子力学物质与量子化辐射场相互作用的标准模型中，开发了方法来表明在可能高度激发态的束缚态制备的孤立原子或分子是不稳定的，并最终通过发射光子松弛到其基态。同样，自由带电粒子的激发态也不稳定。结果表明，当粒子松弛到最小能量状态时，不与电子结合的光子以弹道方式逃逸，随后是软光子云（装扮的单电子态），在这种状态下，它根据简化的动力学传播。对于原子来说，关键问题是要证明没有红外问题发生。对于自由带电粒子，确实会出现红外问题，必须处理CCR的非等效表示。-这些证明需要对Hamilton算符的谱性质有良好的控制，此外还需要相应系统的瑞利散射和康普顿散射的渐近完备性。这些先决条件是由类似于N粒子薛定谔算子的光谱和散射理论的方法和技术所启发的方法和技术建立的，如摩尔理论、传播估计、合适的传播观测值的构造等。此外，还采用了构造量子场论的思想和方法（软光子边界、罗森估计、重整化群分析）。这项研究导致了对原子辐射衰变、光效应和康普顿散射等物理现象在数学上的严格理解。这些现象是许多技术设备的核心，它们决定了我们对世界的视觉印象。此外，辐射衰变现象（或松弛到基态）和在正温度下恢复平衡的类似现象在试图理解开放系统量子理论中的耗散、不可逆行为方面起着关键作用。所开发的数学方法同样适用于其他物理系统，例如晶体中的粒子与量子化晶格振动（声子）相互作用，并且目前应用于研究正温度下物质与辐射相互作用的恢复平衡。