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Article Dans Une Revue Journal of Mathematical Physics Année : 2014

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

Résumé

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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Dates et versions

hal-00943112 , version 1 (12-02-2014)

Identifiants

  • HAL Id : hal-00943112 , version 1

Citer

Konstantin Pankrashkin, Serge Richard. One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results. Journal of Mathematical Physics, 2014, 55 (6), pp.062305. ⟨hal-00943112⟩
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