Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics

We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasi-momentum space the energy spectrum is an overlap of infinitely many inequivalent fractals. The energy levels in each fractal are space-filling curves with Hausdorff dimension 2. The band structure of the spectrum is similar to a fractal spider net in contrast to the Hofstadter butterfly for unbiased motion.Comment: 12 pages, 18 figures. Fractal properties of the energy levels are visualised in the supplementary video material https://www.youtube.com/watch?v=ODS3QVkPTP

Strong-Coupling Perturbation Theory of the Hubbard Model

The strong-coupling perturbation theory of the Hubbard model is presented and carried out to order (t/U)^5 for the one-particle Green function in arbitrary dimension. The spectral weight A(k,omega) is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature--hopping integral (T,t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests of the method are also presented.Comment: 28 pages, 19 figure

Regional Business Networks and the Multinational Retail Sector

In this paper we examine the network relationships of a set of large retail multinational enterprises (MNEs). We analyze under what conditions a flagship-network strategy (characterized by a network of five partners – the MNE; key suppliers; key partners; selected competitors; and key organisations in the non-business infrastructure) explains the internationalisation of three retailers whose geographic scope, sectoral conditions and competitive strategies differ substantially. We explore why and when retailers will adopt a flagship strategy. The three firms are Tesco and The Body Shop, two U.K.-based multinational retailers, and Moet Hennessy Louis Vuitton (LVMH), a French-based global retailer. We find evidence of strong network relationships for all three retailers, yet they embrace network strategies for different reasons. Their flagship relationships depend on each retailer’s strategic use of firm-specific-advantages (FSAs) and country-specific advantages (CSAs). We find that a flagship strategy succeeds in overcoming internal and/or environmental constraints to cross-border resource transfers, which are barriers to foreign direct investment (FDI). We provide recommendations on why and when to use a flagship-based strategy and which type of network partners to prioritize in order to succeed internationally.international retailing, flagship strategy, networks, LVMH, Tesco, The Body Shop, multinational, firm-specific advantages, regional strategy

The SDSS Damped Lya Survey: Data Release 1

We present the results from an automated search for damped Lya (DLA) systems in the quasar spectra of Data Release 1 from the Sloan Digital Sky Survey (SDSS-DR1). At z~2.5, this homogeneous dataset has greater statistical significance than the previous two decades of research. We derive a statistical sample of 71 damped Lya systems (>50 previously unpublished) at z>2.1 and measure HI column densities directly from the SDSS spectra. The number of DLA systems per unit redshift is consistent with previous measurements and we expect our survey has >95% completeness. We examine the cosmological baryonic mass density of neutral gas Omega_g inferred from the damped Lya systems from the SDSS-DR1 survey and a combined sample drawn from the literature. Contrary to previous results, the Omega_g values do not require a significant correction from Lyman limit systems at any redshift. We also find that the Omega_g values for the SDSS-DR1 sample do not decline at high redshift and the combined sample shows a (statistically insignificant) decrease only at z>4. Future data releases from SDSS will provide the definitive survey of DLA systems at z~2.5 and will significantly reduce the uncertainty in Omega_g at higher redshift.Comment: 12 pages, includes color figures. Accepted to PASP, April 20 200

Statistical Assertions for Validating Patterns and Finding Bugs in Quantum Programs

In support of the growing interest in quantum computing experimentation, programmers need new tools to write quantum algorithms as program code. Compared to debugging classical programs, debugging quantum programs is difficult because programmers have limited ability to probe the internal states of quantum programs; those states are difficult to interpret even when observations exist; and programmers do not yet have guidelines for what to check for when building quantum programs. In this work, we present quantum program assertions based on statistical tests on classical observations. These allow programmers to decide if a quantum program state matches its expected value in one of classical, superposition, or entangled types of states. We extend an existing quantum programming language with the ability to specify quantum assertions, which our tool then checks in a quantum program simulator. We use these assertions to debug three benchmark quantum programs in factoring, search, and chemistry. We share what types of bugs are possible, and lay out a strategy for using quantum programming patterns to place assertions and prevent bugs.Comment: In The 46th Annual International Symposium on Computer Architecture (ISCA '19). arXiv admin note: text overlap with arXiv:1811.0544

The ages and metallicities of galaxies in the local universe

We derive stellar metallicities, light-weighted ages and stellar masses for a magnitude-limited sample of 175,128 galaxies drawn from the Sloan Digital Sky Survey Data Release Two (SDSS DR2). We compute median-likelihood estimates of these parameters using a large library of model spectra at medium-high resolution, covering a comprehensive range of star formation histories. The constraints we derive are set by the simultaneous fit of five spectral absorption features, which are well reproduced by our population synthesis models. By design, these constraints depend only weakly on the alpha/Fe element abundance ratio. Our sample includes galaxies of all types spanning the full range in star formation activity, from dormant early-type to actively star-forming galaxies. We show that, in the mean, galaxies follow a sequence of increasing stellar metallicity, age and stellar mass at increasing 4000AA-break strength (D4000). For galaxies of intermediate mass, stronger Balmer absorption at fixed D4000 is associated with higher metallicity and younger age. We investigate how stellar metallicity and age depend on total galaxy stellar mass. Low-mass galaxies are typically young and metal-poor, massive galaxies old and metal-rich, with a rapid transition between these regimes over the stellar mass range 3x10^9<M/Msun<3x10^10. Both high- and low-concentration galaxies follow these relations, but there is a large dispersion in stellar metallicity at fixed stellar mass, especially for low-concentration galaxies of intermediate mass. Despite the large scatter, the relation between stellar metallicity and stellar mass is similar to the correlation between gas-phase oxygen abundance and stellar mass for star-forming galaxies. [abriged]Comment: 22 pages, 14 figures, accepted for publication on MNRAS, data available at http://www.mpa-garching.mpg.de/SDSS

Long Run Macroeconomic Relations in the Global Economy

This paper focuses on testing long run macroeconomic relations for interest rates, equity, prices and exchange rates within a model of the global economy. It considers a number of plausible long run relationships suggested by arbitrage in financial and goods markets, and uses the global vector autoregressive (GVAR) model developed in Dees, di Mauro, Pesaran and Smith (2007) to test for long run restrictions in each country/region conditioning on the rest of the world. Bootstrapping is used to compute both the empirical distribution of the impulse responses and the log-likelihood ratio statistic for over-identifying restrictions. The paper also examines the speed with which adjustments to the long run relations take place via the persistence profiles. We find strong evidence in favour of the uncovered interest parity and to a lesser extent the Fisher equation across a number of countries, but our results for the PPP are much weaker. Also as to be expected, the transmission of shocks and subsequent adjustments in financial markets are much faster than those in goods markets.Global VAR, interdependencies, Fisher relationship, Uncovered Interest Rate Parity, Purchasing Power Parity, persistence profile, error variance decomposition