Directed Wave Propagation in Random Media: Superdiffusion and Phase Transitions

We study a class of classical wave-propagation phenomena in which a multiply scattered wave in a random medium is directed along a certian spatial direction. Such a situation arises in the random scattering systems in which the scattering potential is slowly varying in the z direction. In 2D, we find a superdiffusive transverse displacement of the center of the transmitted beam ${\mathrm{\chi }}_{\mathrm{c}}$∼${\mathrm{z}}^{\mathrm{v}}$ with v≈14, while the width of the beam scales as Δχ∼${\mathrm{z}}^{\mathrm{v}\prime }$ with v′≈12. In 3D, we find a transition: v≈v′≈12 for weak disorder, while v′≈0.46 and v≈0.66 for strong disorder. © 1990 The American Physical Society