Non-Gaussian numerical errors versus mass hierarchy

We probe the numerical errors made in renormalization group calculations by varying slightly the rescaling factor of the fields and rescaling back in order to get the same (if there were no round-off errors) zero momentum 2-point function (magnetic susceptibility). The actual calculations were performed with Dyson's hierarchical model and a simplified version of it. We compare the distributions of numerical values obtained from a large sample of rescaling factors with the (Gaussian by design) distribution of a random number generator and find significant departures from the Gaussian behavior. In addition, the average value differ (robustly) from the exact answer by a quantity which is of the same order as the standard deviation. We provide a simple model in which the errors made at shorter distance have a larger weight than those made at larger distance. This model explains in part the non-Gaussian features and why the central-limit theorem does not apply.Comment: 26 pages, 7 figures, uses Revte

Large thermal Hall coefficient in bismuth

We present a systematical study of thermal Hall effect on a bismuth single crystal by measuring resistivity, Hall coefficient, and thermal conductivity under magnetic field, which shows a large thermal Hall coefficient comparable to the largest one in a semiconductor HgSe. We discuss that this is mainly due to a large mobility and a low thermal conductivity comparing theoretical calculations, which will give a route for controlling heat current in electronic devices.Comment: 4pages, 3 figure

High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model

We calculate the critical exponent gamma of Dyson's hierarchical model by direct fits of the zero momentum two-point function, calculated with an Ising and a Landau-Ginzburg measure, and by linearization about the Koch-Wittwer fixed point. We find gamma= 1.299140730159 plus or minus 10^(-12). We extract three types of subleading corrections (in other words, a parametrization of the way the two-point function depends on the cutoff) from the fits and check the value of the first subleading exponent from the linearized procedure. We suggest that all the non-universal quantities entering the subleading corrections can be calculated systematically from the non-linear contributions about the fixed point and that this procedure would provide an alternative way to introduce the bare parameters in a field theory model.Comment: 15 pages, 9 figures, uses revte

A Guide to Precision Calculations in Dyson's Hierarchical Scalar Field Theory

The goal of this article is to provide a practical method to calculate, in a scalar theory, accurate numerical values of the renormalized quantities which could be used to test any kind of approximate calculation. We use finite truncations of the Fourier transform of the recursion formula for Dyson's hierarchical model in the symmetric phase to perform high-precision calculations of the unsubtracted Green's functions at zero momentum in dimension 3, 4, and 5. We use the well-known correspondence between statistical mechanics and field theory in which the large cut-off limit is obtained by letting beta reach a critical value beta_c (with up to 16 significant digits in our actual calculations). We show that the round-off errors on the magnetic susceptibility grow like (beta_c -beta)^{-1} near criticality. We show that the systematic errors (finite truncations and volume) can be controlled with an exponential precision and reduced to a level lower than the numerical errors. We justify the use of the truncation for calculations of the high-temperature expansion. We calculate the dimensionless renormalized coupling constant corresponding to the 4-point function and show that when beta -> beta_c, this quantity tends to a fixed value which can be determined accurately when D=3 (hyperscaling holds), and goes to zero like (Ln(beta_c -beta))^{-1} when D=4.Comment: Uses revtex with psfig, 31 pages including 15 figure

The Ionizing Source of the Nucleus of NGC1097

We present new observations in X-ray and optical/ultraviolet of the nucleus of NGC1097, known for the abrupt appearance of broad, double-peaked Balmer lines in its spectrum in 1991. These new observations are used to construct the spectral energy distribution (SED) of the central engine. From the SED we infer that this AGN is radio-loud and has a bolometric luminosity L_Bol ~ 10^42 erg/s, implying a low Eddington ratio of L_Bol/L_Edd ~ 10^{-4}. These results suggest that the central ionizing source is an advection-dominated accretion flow (ADAF) in the form of an ellevated structure which photoionizes an outer thin disk. We fit a simplified ADAF model to the SED and obtain limits on the values of the mass accretion rate Mdot and accretion efficiency \eta, namely Mdot/Mdot_Edd >= 10^{-3} and \eta <= 10^{-2}. We identify an energy budget problem: if the central photoionizing source is isotropic, the covering factor of the line-emitting portion of the thin accretion disk is ~ 6, i. e. the central source accounts for only 20% of the energy emitted in the double-peaked Balmer lines.Comment: 4 pages, 3 figures, to appear in the proceedings of "The Interplay among Black Holes, Stars and ISM in Galactic Nuclei", IAU 222, eds. Th. Storchi Bergmann, L.C. Ho, and H.R. Schmit

Microcavity quantum-dot systems for non-equilibrium Bose-Einstein condensation

We review the practical conditions required to achieve a non-equilibrium BEC driven by quantum dynamics in a system comprising a microcavity field mode and a distribution of localised two-level systems driven to a step-like population inversion profile. A candidate system based on eight 3.8nm layers of In(0.23)Ga(0.77)As in GaAs shows promising characteristics with regard to the total dipole strength which can be coupled to the field mode.Comment: 4 pages, 4 figures, to be published in J. Phys. Conf. Ser. for QD201

The Oscillatory Behavior of the High-Temperature Expansion of Dyson's Hierarchical Model: A Renormalization Group Analysis

We calculate 800 coefficients of the high-temperature expansion of the magnetic susceptibility of Dyson's hierarchical model with a Landau-Ginzburg measure. Log-periodic corrections to the scaling laws appear as in the case of a Ising measure. The period of oscillation appears to be a universal quantity given in good approximation by the logarithm of the largest eigenvalue of the linearized RG transformation, in agreement with a possibility suggested by K. Wilson and developed by Niemeijer and van Leeuwen. We estimate $\gamma$ to be 1.300 (with a systematic error of the order of 0.002) in good agreement with the results obtained with other methods such as the $\epsilon$-expansion. We briefly discuss the relationship between the oscillations and the zeros of the partition function near the critical point in the complex temperature plane.Comment: 21 pages, 10 Postcript figures, latex file, uses revte

Friction force microscopy : a simple technique for identifying graphene on rough substrates and mapping the orientation of graphene grains on copper

At a single atom thick, it is challenging to distinguish graphene from its substrate using conventional techniques. In this paper we show that friction force microscopy (FFM) is a simple and quick technique for identifying graphene on a range of samples, from growth substrates to rough insulators. We show that FFM is particularly effective for characterizing graphene grown on copper where it can correlate the graphene growth to the three-dimensional surface topography. Atomic lattice stick–slip friction is readily resolved and enables the crystallographic orientation of the graphene to be mapped nondestructively, reproducibly and at high resolution. We expect FFM to be similarly effective for studying graphene growth on other metal/locally crystalline substrates, including SiC, and for studying growth of other two-dimensional materials such as molybdenum disulfide and hexagonal boron nitride