Strength functions, entropies, and duality in weakly to strongly interacting fermionic systems

Area of Science:

• Quantum mechanics
• Statistical physics
• Atomic physics

Background:

• Statistical wave function properties are crucial for understanding finite systems of interacting fermions.
• Strength functions, participation ratio, and information entropy are key metrics for characterizing these properties.
• The transition from Breit-Wigner to Gaussian forms in strength functions is a known phenomenon in weakly interacting fermions.

Purpose of the Study:

• To revisit and extend the understanding of statistical wave function properties of interacting fermions.
• To propose and utilize an ansatz for the transition of strength functions from Breit-Wigner to Gaussian forms.
• To investigate the behavior of participation ratio and information entropy during this crossover and derive a scaling law.

Main Methods:

• Utilizing strength functions, participation ratio (xi(2)), and information entropy (S(info)).
• Developing an ansatz function to model the Breit-Wigner to Gaussian transition in strength functions.
• Deriving a scaling law for the duality point (lambda(d)) based on the number of fermions (m).

Main Results:

• An ansatz function was proposed to describe the transition of strength functions.
• The study extended the analysis of participation ratio and information entropy into the Breit-Wigner domain.
• A scaling law, lambda(d) approximately 1/sqrt[m], was derived for the duality point where different bases coincide.
• The proposed ansatz successfully described the Breit-Wigner to Gaussian transition in specific neutral atoms (CeI to SmI).

Conclusions:

• The developed ansatz provides a unified description of strength function transitions.
• The derived scaling law offers insights into the duality of fermion system properties.
• The findings have implications for understanding the electronic structure of atoms with changing valence electrons.