Can We Apply Statistical Laws to Small Systems? the Cerium Atom

TL;DR

This paper demonstrates that statistical mechanics can be applied to small quantum systems like the cerium atom, showing how interactions induce equilibrium states but also cause deviations from classical distributions.

Contribution

It provides a theoretical framework for applying statistical laws to finite quantum systems and compares predictions with numerical calculations for cerium.

Findings

Statistical mechanics applies to finite quantum systems with strong residual interactions.

Interaction-induced chaos leads to equilibrium states in small systems.

Deviations from Fermi-Dirac distribution occur due to finite particle number.

Abstract

It is shown that statistical mechanics is applicable to quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, etc., where the residual two-body interaction is sufficiently strong. This interaction mixes the unperturbed shell-model basis states and produces ``chaotic'' many-body eigenstates. As a result, an interaction-induced equilibrium emerges in the system, and temperature can be introduced. However, the interaction between the particles and their finite number can lead to prominent deviations of the equilibrium occupation numbers distribution from the Fermi-Dirac shape. For example, this takes place in the cerium atom with four valence electrons, which was used to compare the theory with realistic numerical calculations.