Resonances in the Two-Centers Coulomb Systems

TL;DR

This paper studies resonances in two-dimensional two-centers Coulomb systems with arbitrary charges, using complex eigenvalues and analytical extensions of the Schrödinger operator to understand their properties.

Contribution

It introduces a novel approach to define and analyze resonances via non-selfadjoint deformations and complex eigenvalues for two-centers Coulomb systems.

Findings

Resonances are characterized as complex eigenvalues on the second Riemann sheet.

Analytic extension of the resolvent kernels is achieved.

Numerical methods support the perturbation theory analysis.

Abstract

We investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalised complex eigenvalues of a non-selfadjoint deformation of the two-centers Schr\"odinger operator. We construct the resolvent kernels of the operators and prove that they can be extended analytically to the second Riemann sheet. The resonances are then analysed by means of perturbation theory and numerical methods.