Repulsion of energies of delocalized states in a double-layer system in a strong magnetic field

A double-layer system in a strong perpendicular magnetic field is considered. Assuming a random potential in each layer to be smooth, we calculate the positions of the delocalized states within a wide range of the tunneling strengths. We show that each delocalized state is composed of alternating pieces of equipotentials from different layers. These combined equipotentials form a percolation network, the nodes of which are the regions where equipotentials from different layers nearly touch each other.