Lyapunov exponent of the random Schrödinger operator with short-range correlated noise potential
We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schrödinger equation with the white noise potential can be expressed through the Lyapunov exponent $γ$ which we determine explicitly as a function of the noise intensity σand the frequency ω. We find uniform two-parameter asymptotic expressions for $γ$ which allow us to evaluate $γ$ for different relations between σand ω. The value of the Lyapunov exponent is also obtained in the case of a short-range correlated noise, which is shown to be less than its white noise counterpart.
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