A General Resonance Theory Based on Mourre’s Inequality
A General Resonance Theory Based on Mourre’s Inequality
复制标题
基于莫雷不等式的一般共振理论
DOI：
10.1007/s00023-005-0261-5
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
W. Hunziker
中科院分区：
文献类型：
--
作者：
L. Cattaneo;G. M. Graf;W. Hunziker
摘要：我们用费米黄金法则研究了连续谱中不稳定的束缚态的微扰。将基于谱变形的共振理论方法推广到一类更一般的量子系统，刻画了预解的光滑性和Mourre不等式性。在微扰理论的框架内，仍然有可能给复共振能和相应的亚稳态的概念赋予明确的含义。主要结果是在摄动理论中得到了高阶受控误差的拟指数衰减估计。
Abstract.We study the perturbation of bound states embedded in the continuous spectrum which are unstable by the Fermi Golden Rule. The approach to resonance theory based on spectral deformation is extended to a more general class of quantum systems characterized by Mourre’s inequality and smoothness of the resolvent. Within the framework of perturbation theory it is still possible to give a definite meaning to the notion of complex resonance energies and of corresponding metastable states. The main result is a quasi-exponential decay estimate up to a controlled error of higher order in perturbation theory.