Wave Packet Dynamics, Ergodicity, and Localization in Quasiperiodic Chains

TL;DR

This study investigates wave packet dynamics in quasiperiodic chains, revealing anomalous diffusion, ergodicity breaking, and the impact of impurities on long-term behavior, using perturbation theory and numerical methods.

Contribution

It introduces a detailed analysis of eigenstates and wave dynamics in quasiperiodic chains, highlighting ergodicity breaking and the role of perturbation order in localization.

Findings

Eigenstates spread across entire chain for v>0

Ergodicity breaks down as v approaches zero

Impurities significantly alter long-term wave dynamics

Abstract

In this paper, we report results for the wave packet dynamics in a class of quasiperiodic chains consisting of two types of weakly coupled clusters. The dynamics are studied by means of the return probability and the mean square displacement. The wave packets show anomalous diffusion in a stepwise process of fast expansion followed by time intervals of confined wave packet width. Applying perturbation theory, where the coupling parameter v is treated as perturbation, the properties of the eigenstates of the system are investigated and related to the structure of the chains. The results show the appearance of non-localized states only in sufficiently high orders of the perturbation expansions. Further, we compare these results to the exact solutions obtained by numerical diagonalization. This shows that eigenstates spread across the entire chain for v>0, while in the limit v->0 ergodicity is broken and eigenstates only spread across clusters of the same type, in contradistinction to trivial localization for v=0. Caused by this ergodicity breaking, the wave packet dynamics change significantly in the presence of an impurity offering the possibility to control its long-term dynamics.