Excited Eigenstates and Strength Functions for Isolated Systems of Interacting Particles

TL;DR

This paper investigates the properties of eigenstates and strength functions in finite, isolated quantum systems of interacting particles, focusing on conditions for ergodicity, quantum chaos, and the transition of eigenstate shapes from Breit-Wigner to Gaussian.

Contribution

It introduces criteria for quantum ergodicity and analyzes the transition of eigenstate shapes in models of interacting particles, highlighting the Gaussian dependence of eigenstate width on energy.

Findings

Eigenstates exhibit chaotic superpositions in finite systems.

Transition from Breit-Wigner to Gaussian shape of eigenstates is characterized.

Eigenstate width depends Gaussianly on energy.

Abstract

Eigenstates in finite systems such as nuclei, atoms, atomic clusters and quantum dots with few excited particles are chaotic superpositions of shell model basis states. We study criterion for the equilibrium distribution of basis components (ergodicity, or Quantum Chaos), effects of level density variation and transition from the Breit-Wigner to the Gaussian shape of eigenstates and strength functions. In the model of $n$ interacting particles distributed over $m$ orbitals, the shape is given by the Breit-Wigner function with the width in the form of gaussian dependence on energy.