Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition

The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the critical level spacing distribution allows to detect with high precision the critical disorder $W_{c}=16.35$. The scaling properties yield the critical exponent, $\nu =1.45 \pm 0.08$, and the disorder dependence of the correlation length.Comment: 11 pages (RevTex), 3 figures included (tar-compressed and uuencoded using UUFILES), to appear in Phys.Rev. B 51 (Rapid Commun.

Delocalization in harmonic chains with long-range correlated random masses

We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations on the random masses landscape. Using a transfer matrix method and exact diagonalization, we compute the localization length and participation ratio of eigenmodes within the band of allowed energies. We find extended vibrational modes in the low-energy region for $\alpha > 1$. In order to study the time evolution of an initially localized energy input, we calculate the second moment $M_2(t)$ of the energy spatial distribution. We show that $M_2(t)$, besides being dependent of the specific initial excitation and exhibiting an anomalous diffusion for weakly correlated disorder, assumes a ballistic spread in the regime $\alpha>1$ due to the presence of extended vibrational modes.Comment: 6 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

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

Dynamics of 2D pancake vortices in layered superconductors

The dynamics of 2D pancake vortices in Josephson-coupled superconducting/normal - metal multilayers is considered within the time-dependent Ginzburg-Landau theory. For temperatures close to $T_{c}$ a viscous drag force acting on a moving 2D vortex is shown to depend strongly on the conductivity of normal metal layers. For a tilted vortex line consisting of 2D vortices the equation of viscous motion in the presence of a transport current parallel to the layers is obtained. The specific structure of the vortex line core leads to a new dynamic behavior and to substantial deviations from the Bardeen-Stephen theory. The viscosity coefficient is found to depend essentially on the angle $\gamma$ between the magnetic field ${\bf B}$ and the ${\bf c}$ axis normal to the layers. For field orientations close to the layers the nonlinear effects in the vortex motion appear even for slowly moving vortex lines (when the in-plane transport current is much smaller than the Ginzburg-Landau critical current). In this nonlinear regime the viscosity coefficient depends logarithmically on the vortex velocity $V$.Comment: 15 pages, revtex, no figure

Diffusion of electrons in random magnetic fields,

Diffusion of electrons in a two-dimensional system in static random magnetic fields is studied by solving the time-dependent Schr\"{o}dinger equation numerically. The asymptotic behaviors of the second moment of the wave packets and the temporal auto-correlation function in such systems are investigated. It is shown that, in the region away from the band edge, the growth of the variance of the wave packets turns out to be diffusive, whereas the exponents for the power-law decay of the temporal auto- correlation function suggest a kind of fractal structure in the energy spectrum and in the wave functions. The present results are consistent with the interpretation that the states away from the band edge region are critical.Comment: 22 pages (8 figures will be mailed if requested), LaTeX, to appear in Phys. Rev.

Energy-level statistics at the metal-insulator transition in anisotropic systems

We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e. weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition using energy-level statistics. The values of the critical disorder $W_c$ are consistent with results of previous studies, including the transfer-matrix method and multifractal analysis of the wave functions. $W_c$ decreases from its isotropic value with a power law as a function of anisotropy. Using high accuracy data for large system sizes we estimate the critical exponent $\nu=1.45\pm0.2$. This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class. The critical level statistics which is independent of the system size at the transition changes from its isotropic form towards the Poisson statistics with increasing anisotropy.Comment: 22 pages, including 8 figures, revtex few typos corrected, added journal referenc

Bond-disordered Anderson model on a two dimensional square lattice - chiral symmetry and restoration of one-parameter scaling

Bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating density of states (DoS), multifractal properties of eigenstates and the localization length. DoS divergence at the band center is studied and compared with Gade's result [Nucl. Phys. B 398, 499 (1993)] and the powerlaw. Although Gade's form describes accurately DoS of finite size systems near the band-center, it fails to describe the calculated part of DoS of the infinite system, and a new expression is proposed. Study of the level spacing distributions reveals that the state closest to the band center and the next one have different level spacing distribution than the pairs of states away from the band center. Multifractal properties of finite systems furthermore show that scaling of eigenstates changes discontinuously near the band center. This unusual behavior suggests the existence of a new divergent length scale, whose existence is explained as the finite size manifestation of the band center critical point of the infinite system, and the critical exponent of the correlation length is calculated by a finite size scaling. Furthermore, study of scaling of Lyapunov exponents of transfer matrices of long stripes indicates that for a long stripe of any width there is an energy region around band center within which the Lyapunov exponents cannot be described by one-parameter scaling. This region, however, vanishes in the limit of the infinite square lattice when one-parameter scaling is restored, and the scaling exponent calculated, in agreement with the result of the finite size scaling analysis.Comment: 23 pages, 11 figures. RevTe

Centring justice in conceptualizing and improving access to urban nature

Environmental Biolog

Leptonic and Semileptonic Decays of Charm and Bottom Hadrons

We review the experimental measurements and theoretical descriptions of leptonic and semileptonic decays of particles containing a single heavy quark, either charm or bottom. Measurements of bottom semileptonic decays are used to determine the magnitudes of two fundamental parameters of the standard model, the Cabibbo-Kobayashi-Maskawa matrix elements $V_{cb}$ and $V_{ub}$. These parameters are connected with the physics of quark flavor and mass, and they have important implications for the breakdown of CP symmetry. To extract precise values of $|V_{cb}|$ and $|V_{ub}|$ from measurements, however, requires a good understanding of the decay dynamics. Measurements of both charm and bottom decay distributions provide information on the interactions governing these processes. The underlying weak transition in each case is relatively simple, but the strong interactions that bind the quarks into hadrons introduce complications. We also discuss new theoretical approaches, especially heavy-quark effective theory and lattice QCD, which are providing insights and predictions now being tested by experiment. An international effort at many laboratories will rapidly advance knowledge of this physics during the next decade.Comment: This review article will be published in Reviews of Modern Physics in the fall, 1995. This file contains only the abstract and the table of contents. The full 168-page document including 47 figures is available at http://charm.physics.ucsb.edu/papers/slrevtex.p