  We study accelerator modes of a particle, confined in an one-dimensional
infinite square well potential, subjected to a time-periodic pulsed field.
Dynamics of such a particle can be described by one generalization of the
kicked rotor. In comparison with the kicked rotor, this generalization is shown
to have a much larger parametric space for existence of the modes. Using this
freedom we provide evidence that accelerator mode assisted anomalous transport
is greatly enhanced when low order resonances are exposed at the border of
chaos. We also present signature of the enhanced transport in the quantum
domain.

Chaotic Dynamics;Quantum Physics