Formulae for partial widths derived from the Lindblad equation

TL;DR

This paper introduces a novel method combining complex scaling techniques with the Lindblad equation to accurately compute partial widths of auto-ionizing states, ensuring trace conservation and consistency with classical rate equations.

Contribution

The paper presents a new approach that integrates complex absorbing potentials or exterior complex scaling with the Lindblad equation for calculating auto-ionizing state widths.

Findings

Method reproduces classical rate equations.

Ensures partial widths sum to total width.

Maintains trace conservation in calculations.

Abstract

A method for calculating partial widths of auto-ionizing states is proposed. It combines either a complex absorbing potential or exterior complex scaling with the Lindblad equation. The corresponding classical rate equations are reproduced, and the trace conservation inherent in the Lindblad equation ensures that the partial widths sums up to the total width of the initial auto-ionizing state.