Spectral isoperimetric inequality for the $\delta'$-interaction on a contour

Vladimir Lotoreichik

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arXiv · 1810.05457

Spectral isoperimetric inequality for the $\delta'$-interaction on a contour

Vladimir Lotoreichik

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Abstract

We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schr\"odinger operator with an attractive $\delta'$-interaction of a fixed strength, the support of which is a $C^2$-smooth contour. Under the constraint of a fixed length of the contour, we prove that the lowest eigenvalue is maximized by the circle. The proof relies on the min-max principle and the method of parallel coordinates.

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BibTeX RIS

Vladimir Lotoreichik. 2018-10-12. Spectral isoperimetric inequality for the $\delta'$-interaction on a contour. https://arxiv.org/abs/1810.05457

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