  As an unusual type of anomalous diffusion behavior, superballistic transport
is not well known but has been experimentally simulated recently. Quantum
superballistic transport models to date are mainly based on connected
sublattices which are constructed to have different properties. In this work,
we show that both quantum and classical superballistic transport in the
momentum space can occur in a simple periodically driven Hamiltonian system,
namely, a relativistic kicked-rotor system with a nonzero mass term. The
nonzero mass term essentially realizes a junction-like scenario: regimes with
low or high momentum values have different dispersion relations and hence
different transport properties. It is further shown that the quantum and
classical superballistic transport should occur under much different choices of
the system parameters. The results are of interest to studies of anomalous
transport, quantum and classical chaos, and the issue of quantum-classical
correspondence.
