  We describe how to engineer wavefunction delocalization in disordered systems
modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically
that a simple product structure for the random onsite potential energies,
together with suitably chosen hopping strengths, allows a resonant scattering
process leading to ballistic transport along one direction, and a controlled
coexistence of extended Bloch states and anisotropically localized states in
the spectrum. We demonstrate that these features persist in the thermodynamic
limit for a continuous range of the system parameters. Numerical results
support these findings and highlight the robustness of the extended regime with
respect to deviations from the exact resonance condition for finite systems.
The localization and transport properties of the system can be engineered
almost at will and independently in each direction. This study gives rise to
the possibility of designing disordered potentials that work as switching
devices and band-pass filters for quantum waves, such as matter waves in
optical lattices.
