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首页> 外文期刊>Annales Henri Poincare >Asymptotic Completeness for Rayleigh Scattering
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Asymptotic Completeness for Rayleigh Scattering

机译：瑞利散射的渐近完备性

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It is expected that the state of an atom or molecule, initially put into an excited state with an energy below the ionization threshold, relaxes to a ground state by spontaneous emission of photons which propagate to spatial infinity. In this paper, this picture is established for a large class of models of non-relativistic atoms and molecules coupled to the quantized radiation field, but with the simplifying feature that an (arbitrarily tiny, but positive) infrared cutoff is imposed on the interaction Hamiltonian. This result relies on a proof of asymptotic completeness for Rayleigh scattering of light on an atom. We establish asymptotic completeness of Rayleigh scattering for a class of model Hamiltonians with the features that the atomic Hamiltonian has point spectrum coexisting with absolutely continuous spectrum, and that either an infrared cutoff is imposed on the interaction Hamiltonian or photons are treated as massive particles. We show that, for models of massless photons, the spectrum of the Hamiltonian strictly below the ionization threshold is purely continuous, except for the ground state energy.
机译：可以预期，最初处于能量低于电离阈值的激发态的原子或分子状态会通过自发发射光子而松弛到基态，该光子传播到空间无穷大。在本文中，该图片是为与耦合到量化辐射场的非相对论性原子和分子的一类大型模型建立的，但是具有简化特征，即对相互作用的哈密顿量施加了一个（任意微小但为正的）红外截止。该结果依赖于光在原子上的瑞利散射的渐近完备性证明。我们建立了一类模型哈密顿量的瑞利散射的渐近完备性，其特征是原子哈密顿量具有与绝对连续光谱共存的点光谱，并且对哈密顿量的相互作用施加了红外截止，或者将光子视为块状粒子。我们表明，对于无质量的光子模型，除了基态能量以外，严格低于电离阈值的哈密顿量光谱是纯连续的。

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