Spectral isoperimetric inequality for the δ'-interaction on a contour

2018/10/12 by Vladimir Lotoreichik, Lotoreichik, Vladimir
Engineering · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Point processes and geometric inequalities #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1810.05457

openalex publication_date 2018/10/12 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrödinger operator with an attractive δ'-interaction of a fixed strength, the support of which is a C²-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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