Wave transmission coefficients for one-dimensional random barriers

The logarithmic decrement $\gamma_D$ is studied for the wave transition coefficient in the case of a long one-dimensional random barrier described by the Markov type potential or by chaotically distributed $\delta$-function-like scatterers. The connection between $\gamma_D$ and $(-1)$ order moment of the amplitude of the Cauchy problem solution of the corresponding Schrödinger equation as well as the Lyapunov coefficient of this equation is established. Some asymptotics of $\gamma_D$ are also found.