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

Reasoning about Data Repetitions with Counter Systems

We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or past. We demonstrate correspondences between satisfiability problems for logics and reachability-like decision problems for counter systems. We show that allowing/disallowing atomic formulas expressing repetitions of values in the past corresponds to the reachability/coverability problem in Petri nets. This gives us 2EXPSPACE upper bounds for several satisfiability problems. We prove matching lower bounds by reduction from a reachability problem for a newly introduced class of counter systems. This new class is a succinct version of vector addition systems with states in which counters are accessed via pointers, a potentially useful feature in other contexts. We strengthen further the correspondences between data logics and counter systems by characterizing the complexity of fragments, extensions and variants of the logic. For instance, we precisely characterize the relationship between the number of attributes allowed in the logic and the number of counters needed in the counter system.Comment: 54 page

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

Molecular Gas in the Powerful Radio Galaxies 3C~31 and 3C~264: Major or Minor Mergers?

We report the detection of $^{12}$CO~($1 \to 0$) and $^{12}$CO~($2 \to 1$) emission from the central regions ($\lesssim 5$--$10 {\rm kpc}$) of the two powerful radio galaxies 3C~31 and 3C~264. Their individual CO emission exhibits a double-horned line profile that is characteristic of an inclined rotating disk with a central depression at the rising part of its rotation curve. The inferred disk or ring distributions of the molecular gas is consistent with the observed presence of dust disks or rings detected optically in the cores of both galaxies. For a CO to H$_2$ conversion factor similar to that of our Galaxy, the corresponding total mass in molecular hydrogen gas is $(1.3 \pm 0.2) \times 10^9 {\rm M_{\odot}}$ in 3C~31 and $(0.31 \pm 0.06) \times 10^9 {\rm M_{\odot}}$ in 3C~264. Despite their relatively large molecular-gas masses and other peculiarities, both 3C~31 and 3C~264, as well as many other powerful radio galaxies in the (revised) 3C catalog, are known to lie within the fundamental plane of normal elliptical galaxies. We reason that if their gas originates from the mergers of two gas-rich disk galaxies, as has been invoked to explain the molecular gas in other radio galaxies, then both 3C~31 and 3C~264 must have merged a long time (a few billion years or more) ago but their remnant elliptical galaxies only recently (last tens of millions of years or less) become active in radio. Instead, we argue that the cannibalism of gas-rich galaxies provides a simpler explanation for the origin of molecular gas in the elliptical hosts of radio galaxies. Given the transient nature of their observed disturbances, these galaxies probably become active in radio soon after the accretion event when sufficient molecular gas agglomerates in their nuclei.Comment: 16 pages, 1 JPEG figure attached, accepted for publication in ApJ

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

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

Identification of New Keynesian Phillips Curves from a Global Perspective

New Keynesian Phillips Curves (NKPC) have been extensively used in the analysis of monetary policy, but yet there are a number of issues of concern about how they are estimated and then related to the underlying macroeconomic theory. The first is whether such equations are identified. To check identification requires specifying the process for the forcing variables (typically the output gap) and solving the model for inflation in terms of the observables. In practice, the equation is estimated by GMM, relying on statistical criteria to choose instruments. This may result in failure of identification or weak instruments. Secondly, the NKPC is usually derived as a part of a DSGE model, solved by log-linearising around a steady state and the variables are then measured in terms of deviations from the steady state. In practice the steady states, e.g. for output, are usually estimated by some statistical procedure such as the Hodrick-Prescott (HP) filter that might not be appropriate. Thirdly, there are arguments that other variables, e.g.interest rates, foreign inflation and foreign output gaps should enter the Phillips curve. This paper examines these three issues and argues that all three benefit from a global perspective. The global perspective provides additional instruments to alleviate the weak instrument problem, yields a theoretically consistent measure of the steady state and provides a natural route for foreign inflation or output gap to enter the NKPC.Global VAR (GVAR), identification, New Keynesian Phillips Curve, Trend-Cycle decomposition