  We investigate the single-particle time evolution and two-particle quantum
correlations in a one-dimensional $N$-site lattice with a site-dependent
nearest neighbor tunneling function $t_\alpha(k)=t_0[k(N-k)]^{\alpha/2}$. Since
the bandwidth and the energy levels spacings for such a lattice both depend
upon $\alpha$, we show that the observable properties of a wavepacket, such as
its spread and the relative phases of its constitutents, vary dramatically as
$\alpha$ is varied from positive to negative values. We also find that the
quantum correlations are exquisitely sensitive to the form of the tunneling
function. Our results suggest that arrays of waveguides with position-dependent
evanascent couplings will show rich dynamics with no counterpart in
present-day, traditional systems.
