Spectral projection, residue of the scattering amplitude, and Schrodinger group expansion for barrie
Spectral projection, residue of the scattering amplitude, and Schrodinger group expansion for barrie
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巴里的光谱投影、散射幅度的残差和薛定谔群展开
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Maher Zerzeri
中科院分区：
文献类型：
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作者：
J. Bony;S. Fujiié;T. Ramond;Maher Zerzeri
我们研究与半经典薛定谔算子的势垒顶共振相关的光谱投影。首先，我们证明了对接近这种共振的复杂能量的可靠估计。使用该估计和共振态的显式表示，我们表明谱投影具有 h 整数幂的半经典展开式，并计算其首项。我们使用这个结果来计算这种共振下的散射幅度的残差。最终，我们根据这些共振给出了薛定谔群的大倍展开。
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrodinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of h, and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we give an expansion for large times of the Schrodinger group in terms of these resonances.