One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results
One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results
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DOI：
10.1063/1.4884417
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发表时间：
2014-02
影响因子：
1.3
通讯作者：
Konstantin Pankrashkin;S. Richard
中科院分区：
文献类型：
--
作者：
Konstantin Pankrashkin;S. Richard
研究了质量为m和零程相互作用的一维Dirac算符的谱和散射理论。给出了波算符和散射算符的显式表达式。这些新公式以一种适当的方式将能量$-\inty$和$+inty$联系起来，并强调了$\pm m$的作用。最后，给出了一个拓扑版的Levinson定理，其中自动考虑了$\pm m$的阈值效应。
The spectral and scattering theory for 1-dimensional Dirac operators with mass $m$ and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new formulae take place in a representation which links, in a suitable way, the energies $-\infty$ and $+\infty$, and which emphasizes the role of $\pm m$. Finally, a topological version of Levinson's theorem is deduced, with the threshold effects at $\pm m$ automatically taken into account.