论文标题
与时间相关的谐波振荡器中的临界散射
Critical scattering in a time-dependent harmonic oscillator
论文作者
论文摘要
受控的时间付费谐波振荡器会改变潜在功能的衰减顺序的阈值，以便存在物理波算子。对于非关键情况，Ishida和Kawamoto \ cite {ik}首先报道了该阈值。在本文中，我们处理关键案例。至于关键案例，情况发生了巨大变化，比非关键案例需要更严格的分析。我们研究这种临界行为，并通过潜在功能的对数增长的力量阐明阈值。因此，该结果揭示了关键案例的量子动力学的渐近学。
Controlled time-decaying harmonic oscillator changes the threshold of decay order of the potential functions in order to exist the physical wave operators. This threshold was first reported by Ishida and Kawamoto \cite{IK} for the non-critical case. In this paper we deal with the critical case. As for the critical case, the situation changes drastically, and much more rigorous analysis is required than that of non-critical case. We study this critical behavior and clarify the threshold by the power of the log growth of the potential functions. Consequently, this result reveals the asymptotics for quantum dynamics of the critical case.
