  We use numerically exact Chebyshev expansion and kernel polynomial methods to
study transport through circular graphene quantum dots in the framework of a
tight-binding honeycomb lattice model. Our focus lies on the regime where
individual modes of the electrostatically defined dot dominate the charge
carrier dynamics. In particular, we discuss the scattering of an injected Dirac
electron wave packet for a single quantum dot, electron confinement in the dot,
the optical excitation of dot-bound modes, and the propagation of an electronic
excitation along a linear array of dots.
