H\"older equicontinuity of the integrated density of states at weak disorder

H\"older continuity, $|N_\lambda(E)-N_\lambda(E')|\le C |E-E'|^\alpha$, with a constant $C$ independent of the disorder strength $\lambda$ is proved for the integrated density of states $N_\lambda(E)$ associated to a discrete random operator $H = H_o + \lambda V$ consisting of a translation invariant hopping matrix $H_o$ and i.i.d. single site potentials $V$ with an absolutely continuous distribution, under a regularity assumption for the hopping term.Comment: 15 Pages, typos corrected, comments and ref. [1] added, theorems 3,4 combine

Benchmarking computer platforms for lattice QCD applications

We define a benchmark suite for lattice QCD and report on benchmark results from several computer platforms. The platforms considered are apeNEXT, CRAY T3E, Hitachi SR8000, IBM p690, PC-Clusters, and QCDOC.Comment: 3 pages, Lattice03, machines and algorithm

On the nature of the FBS blue stellar objects and the completeness of the Bright Quasar Survey. II

In Paper I (Mickaelian et al. 1999), we compared the surface density of QSOs in the Bright Quasar Survey (BQS) and in the First Byurakan Survey (FBS) and concluded that the completeness of the BQS is of the order of 70% rather than 30-50% as suggested by several authors. A number of new observations recently became available, allowing a re-evaluation of this completeness. We now obtain a surface density of QSOs brighter than B = 16.16 in a subarea of the FBS covering ~2250 deg^2, equal to 0.012 deg^-2 (26 QSOs), implying a completeness of 53+/-10%.Comment: LaTeX 2e, 11 pages, 3 tables and 3 figures (included in text). To appear in Astrophysics. Uses a modified aaspp4.sty (my_aaspp4.sty), included in packag

Wave-packet dynamics at the mobility edge in two- and three-dimensional systems

We study the time evolution of wave packets at the mobility edge of disordered non-interacting electrons in two and three spatial dimensions. The results of numerical calculations are found to agree with the predictions of scaling theory. In particular, we find that the $k$-th moment of the probability density $(t)$ scales like $t^{k/d}$ in $d$ dimensions. The return probability $P(r=0,t)$ scales like $t^{-D_2/d}$, with the generalized dimension of the participation ratio $D_2$. For long times and short distances the probability density of the wave packet shows power law scaling $P(r,t)\propto t^{-D_2/d}r^{D_2-d}$. The numerical calculations were performed on network models defined by a unitary time evolution operator providing an efficient model for the study of the wave packet dynamics.Comment: 4 pages, RevTeX, 4 figures included, published versio

Universal asymptotic behavior in flow equations of dissipative systems

Based on two dissipative models, universal asymptotic behavior of flow equations for Hamiltonians is found and discussed. Universal asymptotic behavior only depends on fundamental bath properties but not on initial system parameters, and the integro-differential equations possess an universal attractor. The asymptotic flow of the Hamiltonian can be characterized by a non-local differential equation which only depends on one parameter - independent of the dissipative system or truncation scheme. Since the fixed point Hamiltonian is trivial, the physical information is completely transferred to the transformation of the observables. This yields a more stable flow which is crucial for the numerical evaluation of correlation functions. Furthermore, the low energy behavior of correlation functions is determined analytically. The presented procedure can also be applied if relevant perturbations are present as is demonstrated by evaluating dynamical correlation functions for sub-Ohmic environments. It can further be generalized to other dissipative systems.Comment: 15 pages, 9 figures; to appear in Phys. Rev.

Equivalent Fixed-Points in the Effective Average Action Formalism

Starting from a modified version of Polchinski's equation, Morris' fixed-point equation for the effective average action is derived. Since an expression for the line of equivalent fixed-points associated with every critical fixed-point is known in the former case, this link allows us to find, for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3: published in J. Phys. A - minor change

Influence of disorder on the ferromagnetism in diluted magnetic semiconductors

Influence of disorder on the ferromagnetic phase transition in diluted (III,Mn)V semiconductors is investigated analytically. The regime of small disorder is addressed, and the enhancement of the critical temperature by disorder is found both in the mean field approximation and from the analysis of the zero temperature spin stiffness. Due to disorder, the spin wave fluctuations around the ferromagnetically ordered state acquire a finite mass. At large charge carrier band width, the spin wave mass squared becomes negative, signaling the breakdown of the ferromagnetic ground state and the onset of a noncollinear magnetic order.Comment: Replaced with revised version. 10 pages, 3 figure

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

Interactions, Localization, and the Integer Quantum Hall Effect

We report on numerical studies of the influence of Coulomb interactions on localization of electronic wavefunctions in a strong magnetic field. Interactions are treated in the Hartree-Fock approximation. Localization properties are studied both by evaluating participation ratios of Hartree-Fock eigenfunctions and by studying the boundary-condition dependence of Hartree-Fock eigenvalues. We find that localization properties are independent of interactions. Typical energy level spacings near the Fermi level and the sensitivity of those energy levels to boundary condition show similar large enhancements so that the Thouless numbers of the Hartree-Fock eigenvalues are similar to those of non-interacting electrons.Comment: 10 pages, latex (revtex 3.0), 3 figures are avaiable from S.R. Eric Yang (e-mail [email protected]

Critical regime of two dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates

The critical two-terminal conductance $g_c$ and the spatial fluctuations of critical eigenstates are investigated for a disordered two dimensional model of non-interacting electrons subject to spin-orbit scattering (Ando model). For square samples, we verify numerically the relation $\sigma_c=1/[2\pi(2-D(1))] e^2/h$ between critical conductivity $\sigma_c=g_c=(1.42\pm 0.005) e^2/h$ and the fractal information dimension of the electron wave function, $D(1)=1.889\pm 0.001$. Through a detailed numerical scaling analysis of the two-terminal conductance we also estimate the critical exponent $\nu=2.80\pm 0.04$ that governs the quantum phase transition.Comment: IOP Latex, 7 figure