Numerical verification of universality for the Anderson transition

We analyze the scaling behavior of the higher Lyapunov exponents at the Anderson transition. We estimate the critical exponent and verify its universality and that of the critical conductance distribution for box, Gaussian and Lorentzian distributions of the random potential

Quantum interference and the spin orbit interaction in mesoscopic normal-superconducting junctions

We calculate the quantum correction to the classical conductance of a disordered mesoscopic normal-superconducting (NS) junction in which the electron spatial and spin degrees of freedom are coupled by an appreciable spin orbit interaction. We use random matrix theory to describe the scattering in the normal part of the junction and consider both quasi-ballistic and diffusive junctions. The dependence of the junction conductance on the Schottky barrier transparency at the NS interface is also considered. We find that the quantum correction is sensitive to the breaking of spin rotation symmetry even when the junction is in a magnetic field and time reversal symmetry is broken. We demonstrate that this sensitivity is due to quantum interference between scattering processes which involve electrons and holes traversing closed loops in the same direction. We explain why such processes are sensitive to the spin orbit interaction but not to a magnetic field. Finally we consider the effect of the spin orbit interaction on the phenomenon of ``reflectionless tunnelling.''Comment: Revised version, one new figure and revised text. This is the final version which will appear in Journal de Physqiue 1. Latex plus six postscript figure

Scaling of the conductance distribution near the Anderson transition

The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is essential to investigate the scaling of the full conductance distribution to establish the scaling hypothesis. We present a clear cut numerical demonstration that the conductance distribution indeed obeys one parameter scaling near the Anderson transition

Topology dependent quantities at the Anderson transition

The boundary condition dependence of the critical behavior for the three dimensional Anderson transition is investigated. A strong dependence of the scaling function and the critical conductance distribution on the boundary conditions is found, while the critical disorder and critical exponent are found to be independent of the boundary conditions

Symmetry, dimension and the distribution of the conductance at the mobility edge

The probability distribution of the conductance at the mobility edge, $p_c(g)$, in different universality classes and dimensions is investigated numerically for a variety of random systems. It is shown that $p_c(g)$ is universal for systems of given symmetry, dimensionality, and boundary conditions. An analytical form of $p_c(g)$ for small values of $g$ is discussed and agreement with numerical data is observed. For $g > 1$, $\ln p_c(g)$ is proportional to $(g-1)$ rather than $(g-1)^2$.Comment: 4 pages REVTeX, 5 figures and 2 tables include

Universality of the critical conductance distribution in various dimensions

We study numerically the metal - insulator transition in the Anderson model on various lattices with dimension $2 < d \le 4$ (bifractals and Euclidian lattices). The critical exponent $\nu$ and the critical conductance distribution are calculated. We confirm that $\nu$ depends only on the {\it spectral} dimension. The other parameters - critical disorder, critical conductance distribution and conductance cummulants - depend also on lattice topology. Thus only qualitative comparison with theoretical formulae for dimension dependence of the cummulants is possible

Probability distribution of the conductance at the mobility edge

Distribution of the conductance P(g) at the critical point of the metal-insulator transition is presented for three and four dimensional orthogonal systems. The form of the distribution is discussed. Dimension dependence of P(g) is proven. The limiting cases $g\to\infty$ and $g\to 0$ are discussed in detail and relation $P(g)\to 0$ in the limit $g\to 0$ is proven.Comment: 4 pages, 3 .eps figure

Comment on the paper I. M. Suslov: Finite Size Scaling from the Self Consistent Theory of Localization

In the recent paper [I.M.Suslov, JETP {\bf 114} (2012) 107] a new scaling theory of electron localization was proposed. We show that numerical data for the quasi-one dimensional Anderson model do not support predictions of this theory.Comment: Comment on the paper arXiv 1104.043

Failure of single-parameter scaling of wave functions in Anderson localization

We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1} \times \infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $L \leq 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15 \lesssim -S \lesssim 0.30$ for the range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be published

Immediate effect of kinesiology tape on ankle stability

BackgroundLateral ankle sprain is one of the most common musculoskeletal injuries, particularly among the sporting population. Due to such prevalence, many interventions have been tried to prevent initial, or further, ankle sprains. Current research shows that the use of traditional athletic tape can reduce the incidence of sprain recurrence, but this may be at a cost to athletic performance through restriction of motion. Kinesiology tape, which has become increasingly popular, is elastic in nature, and it is proposed by the manufacturers that it can correct ligament damage. Kinesiology tape, therefore, may be able to improve stability and reduce ankle sprain occurrence while overcoming the problems of traditional tape.AimTo assess the effect of kinesiology tape on ankle stability.Methods27 healthy individuals were recruited, and electromyography (EMG) measurements were recorded from the peroneus longus and tibialis anterior muscles. Recordings were taken from the muscles of the dominant leg during induced sudden ankle inversion perturbations using a custom-made tilting platform system. This was performed with and without using kinesiology tape and shoes, creating four different test conditions: barefoot(without tape), shoe(without tape), barefoot(with tape) and shoe(with tape). For each test condition, the peak muscle activity, average muscle activity and the muscle latency were calculated.ResultsNo significant difference (p&gt;0.05) was found by using the kinesiology tape on any of the measured variables while the wearing of shoes significantly increased all the variables.ConclusionKinesiology tape has no effect on ankle stability and is unable to nullify the detrimental effects that shoes appear to have