# Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems

## TL;DR

This paper investigates how energy eigenstates and eigenvalues differently influence the equilibration of isolated quantum systems, revealing that non-integrable models exhibit non-degenerate energies and 'random' eigenstates that promote equilibration.

## Contribution

It demonstrates the distinct roles of eigen-energies and eigenstates in quantum equilibration, highlighting the importance of non-degeneracy and randomness in non-integrable models.

## Key findings

- Non-integrable models have non-degenerate eigen-energies facilitating rare revivals.
- Energy eigenstates in non-integrable models suppress fluctuations in equilibrium.
- Quantum entropy confirms the 'random' nature of eigenstates, supporting Berry's conjecture.

## Abstract

We show that eigen-energies and energy eigenstates play different roles in the equilibration process of an isolated quantum system. Their roles are revealed numerically by exchanging the eigen-energies between an integrable model and a non-integrable model. We ?find that the structure of eigenenergies of a non-integrable model characterized by non-degeneracy ensures that quantum revival occurs rarely whereas the energy eigenstates of a non-integrable model suppress the fluctuations for the equilibrated quantum state. Our study is aided with a quantum entropy that describes how randomly a wave function is distributed in quantum phase space. We also demonstrate with this quantum entropy the validity of Berry's conjecture for energy eigenstates. This implies that the energy eigenstates of a non-integrable model appear indeed "random".