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.