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

Abstract

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 $\gamma$ which we determine explicitly as a function of the noise intensity σand the frequency ω. We find uniform two-parameter asymptotic expressions for $\gamma$ which allow us to evaluate $\gamma$ 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.

20 pages, 4 figures

References in corpus (2)

• Experimental observation of strong photon localization in disordered photonic crystal waveguides
• The effect of disorder on the wave propagation in one-dimensional periodic optical systems