In this Thesis, the transport behavior of classical wave in 1D random media is studied. Two complementary theories are proposed. One is the self-consistent (SC) diffusion theory while the other is the Dynamic Single-Parameter Scaling (DSPS) model. The validity of each theory in describing the static and dynamic wave propagation is studied. In the static aspect, it is shown that the transport behavior of scattered wave within 1D random media is well described by the SC theory. In the dynamic aspect, the SC theory is also applicable to a certain extent. Since the SC theory does not incorporate the interference effects within the transport mean free path, it cannot describe the localized states with short localization lengths. These localized states dominate the transport behavior in the l...[ Read more ]

In this Thesis, the transport behavior of classical wave in 1D random media is studied. Two complementary theories are proposed. One is the self-consistent (SC) diffusion theory while the other is the Dynamic Single-Parameter Scaling (DSPS) model. The validity of each theory in describing the static and dynamic wave propagation is studied. In the static aspect, it is shown that the transport behavior of scattered wave within 1D random media is well described by the SC theory. In the dynamic aspect, the SC theory is also applicable to a certain extent. Since the SC theory does not incorporate the interference effects within the transport mean free path, it cannot describe the localized states with short localization lengths. These localized states dominate the transport behavior in the long time limit and, therefore, the SC theory fails in the long time limit. On the other hand, the DSPS model describes the system well in all sample sizes, except a short period of early time in which necklace states have significant effects when the sample size is small. For the DSPS model does not consider necklace states, it always underestimates the decay rate in that regime.

Since the SC theory fails at long time scale, any attempt to apply the SC theory on dynamics of wave propagation should be proved for its validity in advance. For the DSPS model, despite the fact that the model is highly simplified, it gives a very good estimation of the dynamic transport behavior at long time. It is shown to be a good picture that gives a suggestive description to the dynamic transport behavior in the localized regime.