Spectral theory for Schr\"odinger operators with $\delta$-interactions supported on curves in $\mathbb R^3$

Jussi Behrndt; Rupert L. Frank; Christian Kühn; Vladimir Lotoreichik; Jonathan Rohleder

doi:10.1007/s00023-016-0532-3

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arXiv · 1601.06433

Spectral theory for Schr\"odinger operators with $\delta$-interactions supported on curves in $\mathbb R^3$

Jussi Behrndt·Rupert L. Frank·Christian Kühn·Vladimir Lotoreichik·Jonathan Rohleder

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Abstract

The main objective of this paper is to systematically develop a spectral and scattering theory for selfadjoint Schr\"odinger operators with $\delta$-interactions supported on closed curves in $\mathbb R^3$. We provide bounds for the number of negative eigenvalues depending on the geometry of the curve, prove an isoperimetric inequality for the principal eigenvalue, derive Schatten--von Neumann properties for the resolvent difference with the free Laplacian, and establish an explicit representation for the scattering matrix.

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BibTeX RIS

Jussi Behrndt, Rupert L. Frank, Christian Kühn, Vladimir Lotoreichik, Jonathan Rohleder. 2016-01-24. Spectral theory for Schr\"odinger operators with $\delta$-interactions supported on curves in $\mathbb R^3$. https://doi.org/10.1007/s00023-016-0532-3

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