Exotic dynamics of excitation in open Aubry-André-Harper model: Effect of the localization, the dimensionality of the environment and the initial condition

H. T. Cui, M. Qin, L. Tang, H. Z. Shen, X. X. Yi

Published 2020-09-13Version 1

The population evolution of excitation is explored in the Aubry-Andr\'{e} model coupled to a $d$-dimensional simple lattices bath, focusing on the effect of localization and the dimensionality of bath, as well as the initial condition. By exact evaluation of the Schr\"{o}dinger equation, the reduced energy levels of the system can be determined, which can be renormalized into the complex ones when the bath is occurring. Furthermore, these complex solutions to Schr\"{o}dinger equation can display different features, according to the dimensionality of bath. As a result, the decaying of excitation in the system can behave very differently; the decaying tends to be super-exponential when $d=1$, in contrast to the exponential decaying when $d=2,3$. In order to gain further understanding of the population evolution of excitation, the propagation of excitation in the lattices bath is also studied in both real and momentum space. It is found that the propagation of excitation in real space can be sub-diffusive or diffusive, according to the initial state. Furthermore, the directional propagation can be observed when the bath is high dimensional. This exotic dynamics of excitation in bath is the manifestation of the distribution of excitation in momentum space, and thus is a result of the interference among the propagating paths. A further analysis discloses that the distribution of excitation in momentum space is determined significantly by the population of the initial state on the energy levels of system. This finding implies that the information of initial state can be recovered by imagining the distribution of excitation in the momentum space of bath.