Influence of two independent sources with long-range correlated disorder in the localization properties of mixed transmission lines

Abstract

We study the localization properties of correlated disordered mixed transmission lines. These systems are formed by the repetition of a set of p successive direct cells followed by q successive dual cells. The spectrum shows a set of d = p + q sub-bands for any kind of disorder where we can find extended and localized states and even gaps. The correlated disorder is introduced only in the capacitances C j , y α , b and inductances L j , y β , b of the dual cells. Meanwhile, the capacitances C j , x and inductances L j , x of the direct cells are kept constant. b measures the amplitude of the disorder, and the correlation exponents α and β quantify the degree of long-range correlation imposed on the system, which is generated by the Fourier filtering method. For fixed p , q and b values it is possible to find extended states as a function of α and β in any of the d sub-bands. For each frequency corresponding to an extended state we can find an asymmetric phase diagram , so that for all α ≥ α c and β ≥ β c with α c ≥ β c , all states are extended. These critical values α c and β c were obtained studying the scaling behavior of the C ω average overlap amplitude. In addition, for fixed α and β , we also find a critical b c value, so for b ≥ b c all states are localized states because the large amplitude b of the fluctuation of the long-range correlated disorder destroys the extended states for all values of α and β . • Mixed transmission lines with p direct cells and q dual cells are studied. • Capacitances an inductances are distributed using two independent sources with long-range correlated disorder. • The localization properties shows an asymmetric phase diagram as a function of the correlation exponent α and β. • The scaling behavior of the C ω average overlap amplitude determines the existence of extended states.