Scattering on compact manifolds with infinitely thin horns
Scattering on compact manifolds with infinitely thin horns
复制标题
具有无限细角的紧凑流形上的散射
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
V. Geyler
中科院分区：
文献类型：
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作者：
J. Bruening;V. Geyler
研究了具有半轴的紧致流形（“刺猬形流形”）上的量子散射。给出了这种流形上Schrodinger算子谱结构的完整描述，证明了散射态的存在性和唯一性，得到了散射矩阵的显式形式，并证明了散射矩阵的么正性.结果表明，初始紧致流形上的Schrodinger算子的谱的正部分以及该算子的点扰动的谱都可以由一个附加半直线的散射振幅恢复.此外，初始薛定谔算子谱的正部分完全由初始流形和连接在其上的两条“线”组成的“电子器件”的电导性质决定。
The quantum-mechanical scattering on a compact manifold with semi-axes attached to the manifold (“hedgehog-shaped manifold”) is considered. The complete description of the spectral structure of Schrodinger operators on such a manifold is done, the proof of existence and uniqueness of scattering states is presented, an explicit form for the scattering matrix is obtained and unitarity of this matrix is proven. It is shown that the positive part of the spectrum of the Schrodinger operator on the initial compact manifold as well as the spectrum of a point perturbation of such an operator may be recovered from the scattering amplitude for one attached half-line. Moreover, the positive part of the spectrum of the initial Schrodinger operator is fully determined by the conductance properties of an “electronic device” consisting of the initial manifold and two “wires” attached to it.