We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent nu for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyze the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent nu=2.73+/-0.02.

We report a numerical study of Anderson localization in a 2D system of non-interacting electrons with spin-orbit coupling. We analyze the scaling of the renormalized localization length for the 2D SU(2) model and estimate its β-function over the full range from the localized to the metallic limits.

Inductively coupled plasma mass spectrometry is introduced as a method for determining the absolute isotopic composition of zinc. The high ionization efficiency and time-independent characteristics of the mass spectrometry permit the absolute isotopic composition of high ionization potential elements. The mass discrimination of the instrument is calibrated by synthetic isotope mixtures prepared from highly enriched isotopes of zinc. The resulting isotope ratios yield atomic percents of 64Zn, 49.188 +/- 0.030; 66Zn, 27.792 +/- 0.041; 67Zn, 4.041 +/- 0.009; 68Zn, 18.378 +/- 0.050; and 70Zn, 0.600 +/- 0.003. This isotopic composition is different from those of conventional mass spectrometric measurements. Their differences depend on the mass differences about 0.8-1.2%/amu with enhancement of heavier isotopes. The atomic weight calculated from our isotopic composition is 65.3756 +/- 0.0040. The obtained atomic weight is fully consistent with that of a precise coulometric measurement in contrast to the previous mass spectrometric measurements. An isotopic variation of commercial zinc reagents has been investigated. A mass-dependent fractionation of 0.12%/amu is observed in a high-purity metal zinc, NIST-SRM 682, among five reagents. This mass dependence is probably inherited through their purification process.

We study the Anderson transition in the SU(2) model and the Ando model. We report a new precise estimate of the critical exponent for the symplectic universality class of the Anderson transition. We also report numerical estimation of the β function.

We report a numerical investigation of the fluctuations of the Lyapunov exponent of a two dimensional non-interacting disordered system. While the ratio of the mean to the variance of the Lyapunov exponent is not constant, as it is in one dimension, its variation is consistent with the single parameter scaling hypothesis.