Peiqing Tong
School of Physics and Technology, 
Nanjing Normal University
pqtong@njnu.edu.cn
Abstract: The anomalous diffusion behaviour has been found in physical, chemical, biological, and even financial systems. Among the various anomalous diffusions, hyperdiffusion ($\gamma>2$) is the most special one and is still less studied. In this talk, I will give our recent work on the spreading of an initially localized electron wave packet in one-dimensional finite sublattices, which are embedded in infinite uniform lattices. We consider the periodic, disordered, and quasiperiodic sublattices, respectively. It is found that there is a transient hyperdiffusion before it ends up in a ballistic diffusion when the potential strength $V$ is less than the critical strength $V_{c}$. When $V=V_{c}$, a transition from diffusion to nondiffusion appears. By studying the energy spectra and eigenstates of the systems, we discuss the reasons of hyperdiffuion and diffusion-nondiffusion transition.