Quantum hall response to time-dependent strain gradients in graphene

Mechanical deformations of graphene induce a term in the Dirac Hamiltonian that is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial energy gaps as indeed observed experimentally. Expanding this analogy, we propose to complement the pseudomagnetic field by a pseudoelectric field, generated by a time-dependent oscillating stress applied to a graphene ribbon. The joint Hall-like response to these crossed fields results in a strain-induced charge current along the ribbon. We analyze in detail a particular experimental implementation in the (pseudo)quantum Hall regime with weak intervalley scattering. This allows us to predict an (approximately) quantized Hall current that is unaffected by screening due to diffusion currents

Running coupling constant and propagators in SU(2) Landau gauge

We present a numerical study of the running coupling constant and of the gluon and ghost propagators in minimal Landau gauge. Simulations are done in pure SU(2) lattice gauge theory for several values of beta and lattice sizes. We use two different lattice setups.Comment: 3 pages and 5 figures; talk presented by A. Cucchieri at Lattice2002(topology), Cambridge MA, USA, June 24-29, 2002 Minor typos correcte

Infrared Exponents and Running Coupling of SU(N) Yang-Mills Theories

We present approximate solutions for the gluon and ghost propagators as well as the running coupling in Landau gauge Yang-Mills theories. We solve the corresponding Dyson-Schwinger equations in flat Euclidean space-time without any angular approximation. This supplements recently obtained results employing a four-torus, i.e. a compact space-time manifold, as infrared regulator. We confirm previous findings deduced from an extrapolation with tori of different volumes: the gluon propagator is weakly vanishing in the infrared and the ghost propagator is highly singular. For non-vanishing momenta our propagators are in remarkable agreement with recent lattice calculations.Comment: 11 pages, 4 figure

Numerical Study of Lattice Landau Gauge QCD and the Gribov Copy Problem

The infrared properties of lattice Landau gauge QCD of SU(3) are studied by measuring gluon propagator, ghost propagator, QCD running coupling and Kugo-Ojima parameter of $\beta=6.0, 16^4,24^4,32^4$ and $\beta=6.4, 32^4, 48^4, 56^4$ lattices. By the larger lattice measurements, we observe that the runnning coupling measured by the product of the gluon dressing function and the ghost dressing function squared rescaled to the perturbative QCD results near the highest lattice momentum has the maximum of about 2.2 at around $q=0.5$ GeV/c, and behaves either approaching constant or even decreasing as $q$ approaches zero. The magnitude of the Kugo-Ojima parameter is getting larger but staying around -0.83 in contrast to the expected value -1 in the continuum theory. We observe, however, there is an exceptional sample which has larger magnitude of the Kugo-Ojima parameter and stronger infrared singularity of the ghost propagator. The reflection positivity of the 1-d Fourier transform of the gluon propagator of the exceptional sample is manifestly violated. Gribov noise problem was studied by performing the fundamental modular gauge (FMG) fixing with use of the parallel tempering method of $\beta=2.2, 16^4$ SU(2) configurations. Findings are that the gluon propagator almost does not suffer noises, but the Kugo-Ojima parameter and the ghost propagator in the FMG becomes $\sim 5$% less in the infrared region than those suffering noises. It is expected that these qualitative aspects seen in SU(2) will reflect in the infrared properties of SU(3) QCD as well.Comment: 6pages, 4 figures, QCDDOWNUNDER conference (2004) proceeding

Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral

It is shown that the study of the imaginary part and of the corresponding dispersion relations of Feynman graph amplitudes within the differential equations method can provide a powerful tool for the solution of the equations, especially in the massive case. The main features of the approach are illustrated by discussing the simple cases of the 1-loop self-mass and of a particular vertex amplitude, and then used for the evaluation of the two-loop massive sunrise and the QED kite graph (the problem studied by Sabry in 1962), up to first order in the (d-4) expansion.Comment: 36 pages, v3 fixed a typo in Eq.(5.5

The Bloch Vector for N-Level Systems

We determine the set of the Bloch vectors for N-level systems, generalizing the familiar Bloch ball in 2-level systems. An origin of the structural difference from the Bloch ball in 2-level systems is clarified.Comment: REVTeX4, 16 pages, 2 EPS figures, add some references, correct some typo

Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum

In this talk we report on a recent lattice investigation of the Landau gauge gluon and ghost propagators in pure SU(3) lattice gauge theory with a special emphasis on the Gribov copy problem. In the (infrared) region of momenta $q^2 \le 0.3 \mathrm{GeV}^2$ we find the corresponding MOM scheme running coupling $\alpha_s(q^2)$ to rise in $q$. We also report on a first SU(3) computation of the ghost-gluon vertex function showing that it deviates only weakly from being constant. In addition we study the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator as well as the spectral representation of the ghost propagator.Comment: talk given by M. M.-P. at the Workshop on Computational Hadron Physics, Cyprus, September 200