Mathematical study of non-relativistic QED: The Link between Resonances and Poles of the Scattering Matrix

非相对论性 QED 的数学研究：共振与散射矩阵极点之间的联系

• 批准号: 350174934
• 负责人: Dr. Dirk - André Deckert
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/350174934?language=en
• 关键词: Mathematical; study; non; relativistic; QED

We will investigate the mathematical relation between resonances and poles of the scattering matrix in non-relativistic quantum electrodynamics (QED). As it is well-understood, non-interacting atomic systems which have stable excited states decay to lower energy states and eventually into the ground state when switching on the interaction with their radiation fields. Mathematically, this behavior can be described by means of eigenstates of non-interacting Hamiltonians turning into resonances. The aim of this project is to provide a rigorous proof of the conjecture that the only poles of the integral kernel of the transition matrix lie at the position of the resonances. In a first part, this behavior shall be proven in the Spin-Boson model. In a second part, the attained results shall be generalized to the Pauli-Fierz model.

我们将研究非相对论量子电动力学（QED）中散射矩阵的共振态和极点之间的数学关系。众所周知，具有稳定激发态的非相互作用原子系统在开启与其辐射场的相互作用时衰减到较低能量状态并最终进入基态。在数学上，这种行为可以通过非相互作用哈密顿量的本征态转变为共振来描述。这个项目的目的是提供一个严格的证明的猜想，唯一的极点的积分核的转移矩阵位于共振的位置。在第一部分中，将在自旋-玻色子模型中证明这种行为。在第二部分中，所获得的结果将被推广到Pauli-Fierz模型。

项目成果

Relation Between the Resonance and the Scattering Matrix in the Massless Spin-Boson Model

无质量自旋玻色子模型中共振与散射矩阵的关系

• DOI: 10.1007/s00220-019-03481-w
• 发表时间: 2019
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: M. Ballesteros;D.-A. Deckert;F. Hänle
• 通讯作者: F. Hänle

One-boson scattering processes in the massive Spin-Boson model

大规模自旋玻色子模型中的单玻色子散射过程

• DOI: 10.1016/j.jmaa.2020.124094
• 发表时间: 2020
• 期刊: Journal of Mathematical Analysis and Applications
• 影响因子: 1.3
• 作者: M. Ballesteros;D.- A. Deckert;J. Faupin;F. Hänle
• 通讯作者: F. Hänle

One-boson scattering processes in the massless Spin-Boson model – A non-perturbative formula

无质量自旋玻色子模型中的单玻色子散射过程 â 非微扰公式

• DOI: 10.1016/j.aim.2020.107248
• 发表时间: 2020
• 期刊: arXiv: Mathematical Physics
• 作者: M. Ballesteros;D.-A. Deckert;J. F. Hänle
• 通讯作者: J. F. Hänle

Analyticity of resonances and eigenvalues and spectral properties of the massless Spin–Boson model

无质量自旋玻色子模型的共振和特征值以及谱特性的解析性

• DOI: 10.1016/j.jfa.2019.02.008
• 发表时间: 2019
• 期刊: Journal of Functional Analysis
• 影响因子: 1.7
• 作者: M. Ballesteros;D.-A. Deckert;F. Hänle
• 通讯作者: F. Hänle