不稳定多能级系统的零能共振与慢衰变
Zero energy resonance and the logarithmically slow decay of unstable multilevel systems
摘要：
基于N-能级Friedrichs模型，研究了不稳定多能级系统约化时间演化算子在零能量共振下的长时间行为，零能量共振意味着预解式在零能量处的发散.借助于Jensen和Kato [Duke Math.J.46，583（1979）]开发的技术，该模型的零能量共振由不属于Hilbert空间的零能量本征态表征。证明了对于某些有理形状因子，约化时间演化算子的渐近慢衰减是可以实现的。
英文摘要：
The long time behavior of the reduced time evolution operator for unstable multilevel systems is studied based on the N-level Friedrichs model in the presence of a zero energy resonance.The latter means the divergence of the resolvent at zero energy. Resorting to the technique developed by Jensen and Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is characterized by the zero energy eigenstate that does not belong to the Hilbert space. It is then shown that for some kinds of the rational form factors the logarithmically slow decay of the reduced time evolution operator can be realized.
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