Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems

TL;DR

This paper investigates how rare quantum eigenstates influence the thermalization process in isolated quantum systems after a sudden change, highlighting finite size effects and proposing scenarios for thermalization.

Contribution

It reveals the role of rare eigenstates in preventing or enabling thermalization, emphasizing finite size effects and contrasting different thermalization scenarios.

Findings

Rare eigenstates can prevent thermalization in integrable models.

Finite size effects significantly influence thermalization outcomes.

Two alternative scenarios for thermalization are discussed.

Abstract

We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In part icular we investigate the pre-requisites for thermalization focusing on the statistical properties of the time-averaged density matrix and o f the expectation values of observables in the final eigenstates. We find that eigenstates, which are rare compared to the typical ones sampled by the micro-canonical distribution, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some non-integrable systems of finite size, such as the Bose-Hubbard model. We stress the importance of finite size effects for the thermalization of isolated quantum systems and discuss two alternative scenarios for thermalization, as well as ways to prune down the correct one.