Spin-dependent electron transport through a ferromagnetic domain wall

We present a theoretical study of spin-dependent transport through a ferromagnetic domain wall. With an increase of the number of components of the exchange coupling, we have observed that the variance of the conductance becomes half. As the strength of the domain wall magnetization is increased, negative magnetoresistance is also observed.Comment: accepted in Proceedings of Localisation 2002 Conference, Tokyo, Japan (to be published as supplement of J. Phys. Soc. Japan

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

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

Anderson transition in the three dimensional symplectic universality class

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 $\beta$ function.Comment: 4 pages, 5 figure

Fluctuations of the Lyapunov exponent in 2D disordered systems

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

What is the right form of the probability distribution of the conductance at the mobility edge?

The probability distribution of the conductance Pc(g) at the Anderson critical point is calculated. It is find that Pc(g) has a dip at small g in agreement with epsilon expansion results. The Pc(g) for the 3d system is quite different from the 2d quantum critical point of the integer quantum Hall effect. The universality or not of these distributions is of central importance to the field of disordered systems.Comment: 1 page, 1 figure submitted to Phys. Rev. Lett. (Comment

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

Kondo-Anderson Transitions

Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metal-insulator transition (AMIT). Critical Power law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature $T_{K}$ is derived at the AMIT, in the metallic phase and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field $B$ and at finite temperature $T$. We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as function of temperature. We find a phase diagram with finite temperature transitions between insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperature-dependent spin-flip scattering rate. Accordingly, we name them Kondo-Anderson transitions (KATs).Comment: 18 pages, 9 figure

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

Spectral Density of the QCD Dirac Operator near Zero Virtuality

We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for an arbitrary number of flavors and zero topological charge. Their microscopic limit provide the master formulae for sum rules for the inverse powers of the eigenvalues of the QCD Dirac operator as recently discussed by Leutwyler and Smilga.Comment: 9 pages + 1 figure, SUNY-NTG-93/