Optimization problem for quantum system with star-shaped potential

Abstract: We discuss the spectral properties of singular Schr\"odinger operators in three dimensions with the interaction supported by an equilateral star. Our main result concerns spectral optimization: we show that the principal eigenvalue is uniquely maximized when the arms are arranged in one of the known five sharp configurations. The results discussed in the talk are the joint work with Pavel Exner.

mathematical physicsanalysis of PDEsspectral theory

Audience: researchers in the topic

Quantum Circle