Dynamical evolution in a one-dimensional incommensurate lattice with PT symmetry
Abstract
We investigate the dynamical evolution of a parity-time (PT) symmetric extension of the Aubry-Andr\'e (AA) model, which exhibits the coincidence of a localization-delocalization transition point with a PT symmetry breaking point. One can apply the evolution of the profile of the wave packet and the long-time survival probability to distinguish the localization regimes in the PT symmetric AA model. The results of the mean displacement show that when the system is in the PT symmetry unbroken regime, the wave-packet spreading is ballistic, which is different from that in the PT symmetry broken regime. Furthermore, we discuss the distinctive features of the Loschmidt echo with the post-quench parameter being localized in different PT symmetric regimes.
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