Arkansas Open Carry: Understanding Law Enforcement’s Legal Capability Under a Difficult Statute

“There seems to us no doubt, on the basis of both text and history, that the Second Amendment conferred an individual right to keep and bear arms.”1 Although the United States Supreme Court in District of Columbia v. Heller established a fundamental understanding that individuals have a right to own a gun for personal use, the Court recognized that, as with all fundamental rights, the individual right to keep and bear arms is “not unlimited.”2 A few limits the Court mentioned included “prohibitions on the possession of firearms by felons and the mentally ill, or laws forbidding the carrying of firearms in sensitive places such as schools and government buildings, or laws imposing conditions and qualifications on the commercial sale of arms.”3 Naturally, the Heller decision left us with this question: What are the constitutionally sound restrictions, and how far can the government go?

Finite pseudo orbit expansions for spectral quantities of quantum graphs

We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and where the total number of bonds is less than or equal to the number of bonds of the graph appear, analogous to a cut off at half the Heisenberg time. The calculation simplifies previous approaches to pseudo orbit expansions on graphs. We formulate coefficients of the characteristic polynomial and derive a secular equation in terms of the irreducible pseudo orbits. From the secular equation, whose roots provide the graph spectrum, the zeta function is derived using the argument principle. The spectral zeta function enables quantities, such as the spectral determinant and vacuum energy, to be obtained directly as finite expansions over the set of short irreducible pseudo orbits.Comment: 23 pages, 4 figures, typos corrected, references added, vacuum energy calculation expande

Semiconductor effective charges from tight-binding theory

We calculate the transverse effective charges of zincblende compound semiconductors using Harrison's tight-binding model to describe the electronic structure. Our results, which are essentially exact within the model, are found to be in much better agreement with experiment than previous perturbation-theory estimates. Efforts to improve the results by using more sophisticated variants of the tight-binding model were actually less successful. The results underline the importance of including quantities that are sensitive to the electronic wavefunctions, such as the effective charges, in the fitting of tight-binding models.Comment: 4 pages, two-column style with 2 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#jb_t

The spin contribution to the form factor of quantum graphs

Following the quantisation of a graph with the Dirac operator (spin-1/2) we explain how additional weights in the spectral form factor K(\tau) due to spin propagation around orbits produce higher order terms in the small-\tau asymptotics in agreement with symplectic random matrix ensembles. We determine conditions on the group of spin rotations sufficient to generate CSE statistics.Comment: 9 page

Quantum indistinguishability from general representations of SU(2n)

A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and Robbins is re-formulated in terms of certain locally flat vector bundles over n-particle configuration space. It is shown how families of such bundles can be constructed from irreducible representations of the group SU(2n). The construction of Berry and Robbins, which leads to a definite connection between spin and statistics (the physically correct connection), is shown to correspond to the completely symmetric representations. The spin-statistics connection is typically broken for general SU(2n) representations, which may admit, for a given value of spin, both bose and fermi statistics, as well as parastatistics. The determination of the allowed values of the spin and statistics reduces to the decomposition of certain zero-weight representations of a (generalised) Weyl group of SU(2n). A formula for this decomposition is obtained using the Littlewood-Richardson theorem for the decomposition of representations of U(m+n) into representations of U(m)*U(n).Comment: 32 pages, added example section 4.

Topological nature of polarization and charge pumping in ferroelectrics

Electric polarization or transferred charge due to an adiabatic change of external parameters $\vec{Q}$ is expressed in terms of a vector field defined in the $\vec{Q}$ space. This vector field is characterized by strings, i.e., trajectories of band-crossing points. In particular, the transverse component is given by the Biot-Savart law in a nonlocal way. For a cyclic change of $\vec{Q}$ along a loop C, the linking number between this string and C represents the amount of the pumped charge, which is quantized to be an integer as discussed by Thouless.Comment: 5 pages including 4 figure

Spectral Statistics for the Dirac Operator on Graphs

We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level statistics are expected, in the semiclassical limit, to correspond to those of random matrices from the Gaussian symplectic ensemble. This is confirmed by numerical investigation. The scattering matrix used to formulate the quantisation condition is found to be independent of the type of spinor. We derive an exact trace formula for the spectrum and use this to investigate the form factor in the diagonal approximation

The Orbital Period and Negative Superhumps of the Nova-Like Cataclysmic Variable V378 Pegasi

A radial velocity study is presented of the cataclysmic variable V378 Pegasi (PG 2337+300). It is found to have an orbital period of 0.13858 +/- 0.00004 d (3.32592 +/- 0.00096 hours). Its spectrum and long-term light curve suggest that V378 Peg is a nova-like variable, with no outbursts. We use the approximate distance and position in the Galaxy of V378 Peg to estimate E(B-V) = 0.095, and use near-infrared magnitudes to calculate a distance of 680 +/- 90 pc and M_V = 4.68 +/- 0.70, consistent with V378 Peg being a nova-like. Time-resolved photometry taken between 2001 and 2009 reveals a period of 0.1346 +/- 0.0004 d (3.23 +/- 0.01 hours). We identify this photometric variability to be negative superhumps, from a precessing, tilted accretion disk. Our repeated measurements of the photometric period of V378 Peg are consistent with this period having been stable between 2001 and 2009, with its negative superhumps showing coherence over as many as hundreds or even thousands of cycles.Comment: 24 pages, 19 figures, accepted for publication in New Astronom

Identifying and prioritising services in European terrestrial and freshwater ecosystems

Ecosystems are multifunctional and provide humanity with a broad array of vital services. Effective management of services requires an improved evidence base, identifying the role of ecosystems in delivering multiple services, which can assist policy-makers in maintaining them. Here, information from the literature and scientific experts was used to systematically document the importance of services and identify trends in their use and status over time for the main terrestrial and freshwater ecosystems in Europe. The results from this review show that intensively managed ecosystems contribute mostly to vital provisioning services (e.g. agro-ecosystems provide food via crops and livestock, and forests provide wood), while semi-natural ecosystems (e.g. grasslands and mountains) are key contributors of genetic resources and cultural services (e.g. aesthetic values and sense of place). The most recent European trends in human use of services show increases in demand for crops from agro-ecosystems, timber from forests, water flow regulation from rivers, wetlands and mountains, and recreation and ecotourism in most ecosystems, but decreases in livestock production, freshwater capture fisheries, wild foods and virtually all services associated with ecosystems which have considerably decreased in area (e.g. semi-natural grasslands). The condition of the majority of services show either a degraded or mixed status across Europe with the exception of recent enhancements in timber production in forests and mountains, freshwater provision, water/erosion/natural hazard regulation and recreation/ecotourism in mountains, and climate regulation in forests. Key gaps in knowledge were evident for certain services across all ecosystems, including the provision of biochemicals and natural medicines, genetic resources and the regulating services of seed dispersal, pest/disease regulation and invasion resistance

Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations

To treat the spectral statistics of quantum maps and flows that are fully chaotic classically, we use the rigorous Riemann-Siegel lookalike available for the spectral determinant of unitary time evolution operators $F$. Concentrating on dynamics without time reversal invariance we get the exact two-point correlator of the spectral density for finite dimension $N$ of the matrix representative of $F$, as phenomenologically given by random matrix theory. In the limit $N\to\infty$ the correlator of the Gaussian unitary ensemble is recovered. Previously conjectured cancellations of contributions of pseudo-orbits with periods beyond half the Heisenberg time are shown to be implied by the Riemann-Siegel lookalike