Interaction between randomly charged rods and plates: Energy landscapes, stick slip, and recognition at a distance

We study the interaction between randomly, irreversibly charged objects. We consider arbitrary relative displacements of two parallel rigid rods and of two parallel rigid plates, and calculate the statistical properties of the resulting energy landscape, such as the distribution of the energies of potential minima and maxima, the depth, the radia of curvature, and the width and density of typical energy wells, as functions of the separation between the objects and of the Debye screening length. We show that this complicated energy landscape may lead to stick-slip phenomena during relative displacement of the plates. We study the case of perfectly correlated charge distributions on the two objects, and show that the presence of long range forces may lead to prealignment of the objects, even before contact. The relevance of our results to interacting biological systems and to pattern recognition is discussed.