ON THE RELATIONSHIPS BETWEEN SPATIAL CLUSTERING, INEQUALITY, AND ECONOMIC GROWTH IN THE UNITED STATES : 1969-2000

The literature on economic development has been divided as to the nature of the relationship between inequality and growth. Recent exploratory work in the field has provided evidence that the dynamic and spatial relationships between the two may be far more complicated than previously thought. This paper provides an spatial econometric specification for the analysis of economic growth, that allows for simultaneity as it relates to inequality. Furthermore, attention is given to the possible impacts of local clustering on the performance of individual economies in a global setting. The new methodology is applied to the US states from 1969–2000, where the counties are used for the local inequality and clustering estimates.ECONOMIC GROWTH, INEQUALITY, SIMULTANEITY, SPATIAL CLUSTERING

Spatial Clustering, Inequality and Income Convergence

This paper examines the relationship between spatial clustering and inequality at the county scale with overall state per capita income in the U.S. over the period 1969-2000. For each of the 48 coterminous states we examine measures of inequality and spatial clustering and explore how a state's overall income level may be influenced by, or influence, these measures. Our exploratory analysis utilizes the open- source package Space-Time Analysis of Regional Systems (STARS) to illustrate some new techniques for analyzing regional income dynamics. The results provide insight into the possible relationships between inequality, clustering and relative income levels, and generates a number of interesting avenues for future research.spatial clustering; spatial dependence; inequality; convergence; geocomputation

Closed Spaces in Cosmology

This paper deals with two aspects of relativistic cosmologies with closed (compact and boundless) spatial sections. These spacetimes are based on the theory of General Relativity, and admit a foliation into space sections S(t), which are spacelike hypersurfaces satisfying the postulate of the closure of space: each S(t) is a 3-dimensional, closed Riemannian manifold. The discussed topics are: (1) A comparison, previously obtained, between Thurston's geometries and Bianchi-Kantowski-Sachs metrics for such 3-manifolds is here clarified and developed. (2) Some implications of global inhomogeneity for locally homogeneous 3-spaces of constant curvature are analyzed from an observational viewpoint.Comment: 20 pages, 6 figures, revised version of published paper. In version 2: several misprints corrected, 'redshifting' in figures improved. Version 3: a few style corrections; couple of paragraphs in subsection 2.4 rewritten. Version 4: figures 5 and 6 corrrecte

Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid

We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely. In a large-N limit, we find a chiral spin liquid ground state with topological order and Abelian fractional statistics. We discuss its experimental detection. Chiral spin liquids with non-Abelian anyons may also be realizable with alkaline earth atoms.Comment: 4 pages, 2 figures, 1 table. Minor changes from v2. Final published versio

Beyond the Spin Model Approximation for Ramsey Spectroscopy

Ramsey spectroscopy has become a powerful technique for probing non-equilibrium dynamics of internal (pseudospin) degrees of freedom of interacting systems. In many theoretical treatments, the key to understanding the dynamics has been to assume the external (motional) degrees of freedom are decoupled from the pseudospin degrees of freedom. Determining the validity of this approximation -- known as the spin model approximation -- is complicated, and has not been addressed in detail. Here we shed light in this direction by calculating Ramsey dynamics exactly for two interacting spin-1/2 particles in a harmonic trap. We focus on $s$-wave-interacting fermions in quasi-one and two-dimensional geometries. We find that in 1D the spin model assumption works well over a wide range of experimentally-relevant conditions, but can fail at time scales longer than those set by the mean interaction energy. Surprisingly, in 2D a modified version of the spin model is exact to first order in the interaction strength. This analysis is important for a correct interpretation of Ramsey spectroscopy and has broad applications ranging from precision measurements to quantum information and to fundamental probes of many-body systems

Hanbury Brown-Twiss Interferometry for Fractional and Integer Mott Phases

Hanbury-Brown-Twiss interferometry (HBTI) is used to study integer and fractionally filled Mott Insulator (MI) phases in period-2 optical superlattices. In contrast to the quasimomentum distribution, this second order interferometry pattern exhibits high contrast fringes in the it insulating phases. Our detailed study of HBTI suggests that this interference pattern signals the various superfluid-insulator transitions and therefore can be used as a practical method to determine the phase diagram of the system. We find that in the presence of a confining potential the insulating phases become robust as they exist for a finite range of atom numbers. Furthermore, we show that in the trapped case the HBTI interferogram signals the formation of the MI domains and probes the shell structure of the system.Comment: 13 pages, 15 figure