Spectral isoperimetric inequality for the $\delta'$-interaction on a contour
Spectral Theory
2018-10-15 v1 Mathematical Physics
math.MP
Abstract
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schr\"odinger operator with an attractive -interaction of a fixed strength, the support of which is a -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.
Keywords
Cite
@article{arxiv.1810.05457,
title = {Spectral isoperimetric inequality for the $\delta'$-interaction on a contour},
author = {Vladimir Lotoreichik},
journal= {arXiv preprint arXiv:1810.05457},
year = {2018}
}
Comments
contribution to the proceedings of the 3rd workshop "Mathematical Challenges of Zero-Range Physics: rigorous results and open problems"