Complex absorbing potential method for Stark resonances

TL;DR

This paper demonstrates that Stark resonances can be characterized as the limit of complex eigenvalues of a Stark Hamiltonian with a quadratic complex absorbing potential, using complex distortion techniques.

Contribution

It introduces a method to characterize Stark resonances via complex absorbing potentials, extending to potentials with local singularities like Coulomb.

Findings

Stark resonances are limit points of eigenvalues with absorbing potential

The method applies to potentials with Coulomb-like singularities

Uses complex distortion outside a cone for proof

Abstract

We characterize the resonances of Stark Hamiltonians by the complex absorbing potential method. Namely, we prove that the Stark resonances are the limit points of complex eigenvalues of the Stark Hamiltonian with a quadratic complex absorbing potential when the absorbing coefficient tends to zero. The proof employs the complex distortion outside a cone introduced in the previous work by the author. Potentials with local singularities such as the Coulomb potential are allowed as perturbations.