Percolation Transition Control in Quantum Networks

Abstract

Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the percolation transition for a chosen occupation probability has been an open problem. At the same time, the task to find a structurally simple network having the desired property seemed to be impossible. I suggest a model, where the combination of the classical and the quantum resources creates a percolation transition, continuous or discontinuous on demand, for any pre-selected occupation probability and already in the simplest possible one-dimensional network.