Lyapunov exponent in two-leg ladder model

Lyapunov exponent is one of the properties to study localization-delocalization transition in disordered systems. Perfect as well as disordered two-leg ladder is studied in tight-binding description. In perfectly two-leg ladder two bands are obtained due to symmetric and antisymmetric wave functions. But, the analytical expression of Lyapunov exponent indicates the presence of extended states at the overlapping region of two bands. Beyond this region of energy states are localized. Two models of disordered ladder network are studied here numerically. These studies show that the Lyapunov exponent indicates the presence of extended states provided both the even and odd modes are extended in transmission analysis. If the transmission coefficient shows the localization behavior for one of the modes the Lyapunov exponent also indicates the localization of those states. The behavior of first Lyapunov exponent is consistent with that of the Lyapunov exponent. on the other hand, the study of second Lyapunov exponent is consistent with the transmission analysis.