Spectral analysis and time-dependent scattering theory on manifolds with asymptotically cylindrical ends
Spectral analysis and time-dependent scattering theory on manifolds with asymptotically cylindrical ends
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渐近圆柱端流形的谱分析和瞬态散射理论
DOI：
10.1142/s0129055x13500037
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
R. T. Aldecoa
中科院分区：
文献类型：
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作者：
Serge Richard;R. T. Aldecoa
我们回顾了具有渐近圆柱末端的歧管的频谱分析和散射理论的时间依赖方法。对于光谱分析，通过Mourre理论获得了高阶分解估计值，用于公制的短距离和远程行为以及无穷大的扰动。对于散射理论，在两个希尔伯特的空间设置中证明了波动算子的存在和渐近完整性。得出了一个固定公式以及散射操作员的映射属性。时间延迟的存在及其与EisenBud-Wigner时间延迟的平等最终得出。我们的分析主要不同于现有的文献，关于选择更简单的比较动力学以及有关时间依赖性和固定散射理论的互补使用。
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity. For the scattering theory, the existence and asymptotic completeness of the wave operators is proved in a two-Hilbert spaces setting. A stationary formula as well as mapping properties for the scattering operator are derived. The existence of time delay and its equality with the Eisenbud-Wigner time delay is finally presented. Our analysis mainly differs from the existing literature on the choice of a simpler comparison dynamics as well as on the complementary use of time-dependent and stationary scattering theories.