The scaling of the density of states in systems with resonance states

TL;DR

This paper investigates how the density of states in two-electron quantum dots behaves near resonances, revealing critical behavior through numerical methods and analyzing resonance energies and lifetimes.

Contribution

It introduces a combined variational and complex scaling approach to study the density of states and its critical behavior in quantum dot resonance phenomena.

Findings

Density of states shows critical dependence on basis-set size near resonances

Resonance energies and lifetimes are extracted from scaling properties

Numerical evidence supports the critical behavior of the density of states

Abstract

Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states in the region where there are resonances. The critical behavior is signaled by a strong dependence of some features of the density of states with the basis-set size used to calculate it. The resonance energy and lifetime are obtained using the scaling properties of the density of states