We study the randomness effects and the magneto-properties of quasi-one- dimensional disordered systems. We find that in the random magnetic field (RMF) systems the randomness effect on the localization length is not universal. We find that the localization length is not a monotonic decreasing function of magnetic field randomness δ. This is in contrast to the Anderson model in which the localization length is a monotonic decreasing function of the Anderson ran-domness w. An interesting observation is made on the magnetoproperties of the localization length in both RMF systems and Anderson systems. We find that the localization length can both increase and decrease with uniform magnetic field depending on the energy of state. The crossover occurs when the electron energy is close to th...[ Read more ]

We study the randomness effects and the magneto-properties of quasi-one- dimensional disordered systems. We find that in the random magnetic field (RMF) systems the randomness effect on the localization length is not universal. We find that the localization length is not a monotonic decreasing function of magnetic field randomness δ. This is in contrast to the Anderson model in which the localization length is a monotonic decreasing function of the Anderson ran-domness w. An interesting observation is made on the magnetoproperties of the localization length in both RMF systems and Anderson systems. We find that the localization length can both increase and decrease with uniform magnetic field depending on the energy of state. The crossover occurs when the electron energy is close to the band edge. For the RMF system, the magneto-property of the localization length is even more complicated throughout the entire energy band. We propose a band edge effect for explaining the anomalous magneto-properties of the localization length. In additional to the numerical results, we formulate the calculation of localization length into the calculation of the Lyapunov exponents of a product of random matrices. Then we use mean field theory to calculate the Lyapunov exponents. We conjecture that for the case of a real independent random matrix, this mean field approach gives the upper bound of the maximum Lyapunov exponent.