Conducting to non-conducting transition in dual transmission lines using a ternary model with long-range correlated disorder

In this work we study the behavior of the allowed and forbidden frequencies in disordered classical dual transmission lines when the values of capacitances {Cj} are distributed according to a ternary model with long-range correlated disorder. We introduce the disorder from a random sequence with a power spectrum S(k)∝k−(2α−1), where α?0.5 is the correlation exponent. From this sequence we generate an asymmetric ternary map using two map parameters b₁ and b₂, which adjust the occupancy probability of each possible value of the capacitances Cj={CA,CB,CC,}. If the sequence of capacitance values is totally at random α=0.5 (white noise), the electrical transmission line is in the non-conducting state for every frequency ω. When we introduce long-range correlations in the distribution of capacitances, the electrical transmission lines can change their conducting properties and we can find a transition from the non-conducting to conducting state for a fixed system size. This implies the existence of critical values of the map parameters for each correlation exponent α. By performing finite-size scaling we obtain the asymptotic value of the map parameters in the thermodynamic limit for any α. With these data we obtain a phase diagram for the symmetric ternary model, which separates the non-conducting state from the conducting one. This is the fundamental result of this Letter. In addition, introducing one or more impurities in random places of the long-range correlated distribution of capacitances, we observe a dramatic change in the conducting properties of the electrical transmission lines, in such a way that the system jumps from conducting to non-conducting states. We think that this behavior can be considered as a possible mechanism to secure communication.