Open dynamics in the Aubry-Andr\'{e}-Harper model coupled to a finite bath: the influence of localization in the system and dimensionality of bath

TL;DR

This study investigates how the localization properties of the Aubry-André-Harper model are affected by coupling to finite-dimensional baths, revealing dimension-dependent decay and spreading behaviors of excitation.

Contribution

It provides a detailed analysis of excitation dynamics in the AAH model coupled to baths of different dimensions, highlighting the influence of bath dimensionality on localization and decay.

Findings

Excitation decay is super-exponential for 1D baths.

Excitation decay is exponential for 2D and 3D baths.

Spreading in the bath can be diffusive or localized depending on conditions.

Abstract

The population evolution of single excitation is studied in the Aubry- Andr\'{e}- Harper (AAH) model coupled to a $d (=1,2,3)$-dimensional simple lattices bath with a focus on the effect of localization in the system and the dimensionality of bath. By performing a precise evaluation of time-independent Schr\"{o}dinger equation, the reduced energy levels of the system can be determined. It is found that the reduce energy levels show significant relevance for the bath dimensions. Subsequently, the time evolution of excitation is studied in both the system and bath. It is found that excitation in the system can decay super-exponentially when $d=1$ or exponentially when $d=2,3$. Regarding the finite nature of bath, the spreading of excitation in the lattices bath is also studied. We find that, depending on the dimensions of bath and the initial state, the spreading of excitation in the bath is diffusive or behaves localization.