In a multi-layer medium with lateral inhomogeneities, electron wavefunctions decay exponentially in the lateral direction due to it Anderson localization. Chanels are defined in the layering direction. Channel hopping occurs due to isotropic scatterings via the evanescent channels as well as the overlap of wavefunctions in different channels. It is found that the relative electron probability becomes a steady state after some length, which is called the it equilibration length L_eq. This result is independent of which channel the electron is being injected into. In the presence of evanescent channel, a dominant channel can exist. To study the effect of evanescent channels to the equilibration length, we considered the cases with potential barriers between channels. It is found that L...[ Read more ]

In a multi-layer medium with lateral inhomogeneities, electron wavefunctions decay exponentially in the lateral direction due to it Anderson localization. Chanels are defined in the layering direction. Channel hopping occurs due to isotropic scatterings via the evanescent channels as well as the overlap of wavefunctions in different channels. It is found that the relative electron probability becomes a steady state after some length, which is called the it equilibration length L_eq. This result is independent of which channel the electron is being injected into. In the presence of evanescent channel, a dominant channel can exist. To study the effect of evanescent channels to the equilibration length, we considered the cases with potential barriers between channels. It is found that L_eq [proportional to] Ln(W_b[susperscript 2]), where W_b is the barrier height. The logarithmic behavior can be understood by adopting the master equations approach.

A systematic way is proposed to determine all the Lyapunov exponents from the transmission coefficients T_ij of the system, so that the measurement of Lyapunov exponents now becomes possible, e.g. in acoustic waves or elastic waves. The dependence of various Lyapunov exponents and equilibration lengths on the randomness is also studied for both cases with and without potential barriers.