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arXiv · 1402.1542

One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results

K. Pankrashkin·S. Richard
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Abstract

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.

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K. Pankrashkin, S. Richard. 2014-02-07. One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results. https://doi.org/10.1063/1.4884417

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