Localization in a chain with periodically moving quasi-periodic potential

Abstract We study the localization feature of a one dimensional lattice in the presence of a periodically moving quasi-periodic potential. In the case of a strong quasi-periodic potential such that the system is in the localized phase when the potential is static, we find that the system remains localized until the moving range of the potential is large enough. For a static delocalized system with weak quasi-periodic potential, we show the existence of a parameter window for the moving range and moving frequency of the potential, within which part of the states in the system are localized. In the delocalized phase induced by the periodically moving of the quasi-periodic potential, we find that the wave packet spreading with a low frequency moving potential is much slowly than the high frequency situation. If the system is in the partially localized phase with a weak moving quasi-periodic potential, we find the spreading of the wave packet is ballistic and the inverse participation ratio of the system state remains a larger value when the initial state has a large overlap with the localized eigenstates of the stroboscopic time evolution operator.