Thursday, June 6, 2013

1104.3150 (Yuri Godin et al.)

Lyapunov exponent of the random Schrödinger operator with
short-range correlated noise potential

Yuri Godin, Stanislav Molchanov, Boris Vainberg
We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schr\"{o}dinger equation with the white noise potential can be expressed through the Lyapunov exponent $\gamma$ which we determine explicitly as a function of the noise intensity \sigma and the frequency \omega. We find uniform two-parameter asymptotic expressions for $\gamma$ which allow us to evaluate $\gamma$ for different relations between \sigma and \omega. 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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