Asymptotic Completeness for Rayleigh Scattering
Asymptotic Completeness for Rayleigh Scattering
复制标题
瑞利散射的渐近完备性
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Benjamin Schlein
中科院分区：
文献类型：
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作者：
J. Frölich;M. Griesemer;Benjamin Schlein
摘要。原子或分子最初处于能量低于电离阈值的激发态，由于光子的自发发射而松弛到基态，光子传播到无限空间。本文建立了一大批与量子化辐射场耦合的非相对论性原子和分子模型的这幅图，但其简化特征是在相互作用哈密顿量上施加了一个（任意微小但正的）红外截止。这个结果依赖于光在原子上的瑞利散射的渐近完备性的证明。本文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点谱与绝对连续谱共存的特点，或者在相互作用哈密顿量上施加红外截止，或者将光子作为大质量粒子处理。我们证明，对于无质量光子模型，严格低于电离阈值的哈密顿谱是纯连续的，除了基态能量。
Abstract. 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.