An isoperimetric problem for point interactions

Abstract

We consider Hamiltonian with $N$ point interactions in ${\mathbb{R}}^d,d=2,3,$ all with the same coupling constant, placed at vertices of an equilateral polygon $\PP_N$. It is shown that the ground state energy is locally maximized by a regular polygon. The question whether the maximum is global is reduced to an interesting geometric problem.

LaTeX 2e, 10 pages

References in corpus (3)

• Geometrically induced spectrum in curved leaky wires
• Leaky quantum graphs: approximations by point interaction Hamiltonians
• Bound states of infinite curved polymer chains

Cited by in corpus (5)

• An isoperimetric problem for leaky loops and related mean-chord inequalities
• Inequalities for means of chords, with application to isoperimetric problems
• A spectral isoperimetric inequality for cones
• Equilibria of point charges on convex curves
• Equilibria of three constrained point charges