Two-parameter asymptotics of the Lyapunov exponent of the random Schrödinger operator

Details Two-parameter asymptotics of the Lyapunov exponent of the random Schrödinger operator Two-parameter asymptotics of the Lyapunov exponent of the random Schrödinger operator

2011-04-15

arxiv.org/abs/1104.3150v2

Physics

Mathematical Physics

14 pages, 4 figures

Scientific paper

We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties can be expressed through the Lyapunov exponent. We give an explicit formula for the Lyapunov exponent $\gamma$ of the Schr\"{o}dinger equation with the white noise potential as a function of the noise intensity $\sigma$ and the frequency $\omega$. We find uniform two-parameter asymptotic expressions of $\gamma$ which allows us to evaluate it for different relations between $\sigma$ and $\omega$.

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