In this paper we have investigated chain mobility in polyethylene below its melting temperature. The investigation techniques like atomic force microscopy (AFM), transmission electron microscopy (TEM), time-resolved small/wide angle X-ray scattering (SAXS/WAXS), time-resolved longitudinal acoustic mode (LAM) Raman spectroscopy have been used to follow the chain mobility within individual single crystals and regularly stacked crystals, as a function of temperature and time. Our observations on single crystals are that crystal thickness increases immediately on heating just above the crystallization temperature. In the regularly stacked polyethylene single crystals wherever the overlapping of at least two lamellae arises, thickening occurs during annealing via a mutual chain rearrangement between the adjacent crystals, which leads (ultimately) to a quantum increase, i.e., doubling, of the lamellar thickness. A model has been proposed to explain this quantum increase in the lamellar thickness. The fundamental findings have been extended for some applications.