A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

Density Waves in Layered Systems with Fermionic Polar Molecules

A layered system of two-dimensional planes containing fermionic polar molecules can potentially realize a number of exotic quantum many-body states. Among the predictions, are density-wave instabilities driven by the anisotropic part of the dipole-dipole interaction in a single layer. However, in typical multilayer setups it is reasonable to expect that the onset and properties of a density-wave are modified by adjacent layers. Here we show that this is indeed the case. For multiple layers the critical strength for the density-wave instability decreases with the number of layers. The effect depends on density and is more pronounced in the low density regime. The lowest solution of the instability corresponds to the density waves in the different layers being in-phase, whereas higher solutions have one or several adjancet layers that are out of phase. The parameter regime needed to explore this instability is within reach of current experiments.Comment: 7 pages, 4 figures. Final version in EPJD, EuroQUAM special issue "Cold Quantum Matter - Achievements and Prospects

A Theory for High-TcT_c Superconductors Considering Inhomogeneous Charge Distribution

We propose a general theory for the critical $T_c$ and pseudogap $T^*$ temperature dependence on the doping concentration for high-$T_c$ oxides, taking into account the charge inhomogeneities in the $CuO_2$ planes. The well measured experimental inhomogeneous charge density in a given compound is assumed to produce a spatial distribution of local $\rho(r)$. These differences in the local charge concentration is assumed to yield insulator and metallic regions, possibly in a stripe morphology. In the metallic region, the inhomogeneous charge density yields also spatial distributions of superconducting critical temperatures $T_c(r)$ and zero temperature gap $\Delta_0(r)$. For a given sample, the measured onset of vanishing gap temperature is identified as the pseudogap temperature, that is, $T^*$, which is the maximum of all $T_c(r)$. Below $T^*$, due to the distribution of $T_c(r)$'s, there are some superconducting regions surrounded by insulator or metallic medium. The transition to a superconducting state corresponds to the percolation threshold among the superconducting regions with different $T_c(r)$'s. To model the charge inhomogeneities we use a double branched Poisson-Gaussian distribution. To make definite calculations and compare with the experimental results, we derive phase diagrams for the BSCO, LSCO and YBCO families, with a mean field theory for superconductivity using an extended Hubbard Hamiltonian. We show also that this novel approach provides new insights on several experimental features of high-$T_c$ oxides.Comment: 7 pages, 5 eps figures, corrected typo

Thermodynamics of Dipolar Chain Systems

The thermodynamics of a quantum system of layers containing perpendicularly oriented dipolar molecules is studied within an oscillator approximation for both bosonic and fermionic species. The system is assumed to be built from chains with one molecule in each layer. We consider the effects of the intralayer repulsion and quantum statistical requirements in systems with more than one chain. Specifically, we consider the case of two chains and solve the problem analytically within the harmonic Hamiltonian approach which is accurate for large dipole moments. The case of three chains is calculated numerically. Our findings indicate that thermodynamic observables, such as the heat capacity, can be used to probe the signatures of the intralayer interaction between chains. This should be relevant for near future experiments on polar molecules with strong dipole moments.Comment: 15 pages, 5 figures, final versio

Mapping the Two-Component Atomic Fermi Gas to the Nuclear Shell-Model

The physics of a two-component cold fermi gas is now frequently addressed in laboratories. Usually this is done for large samples of tens to hundreds of thousands of particles. However, it is now possible to produce few-body systems (1-100 particles) in very tight traps where the shell structure of the external potential becomes important. A system of two-species fermionic cold atoms with an attractive zero-range interaction is analogous to a simple model of nucleus in which neutrons and protons interact only through a residual pairing interaction. In this article, we discuss how the problem of a two-component atomic fermi gas in a tight external trap can be mapped to the nuclear shell model so that readily available many-body techniques in nuclear physics, such as the Shell Model Monte Carlo (SMMC) method, can be directly applied to the study of these systems. We demonstrate an application of the SMMC method by estimating the pairing correlations in a small two-component Fermi system with moderate-to-strong short-range two-body interactions in a three-dimensional harmonic external trapping potential.Comment: 13 pages, 3 figures. Final versio

The First VERITAS Telescope

The first atmospheric Cherenkov telescope of VERITAS (the Very Energetic Radiation Imaging Telescope Array System) has been in operation since February 2005. We present here a technical description of the instrument and a summary of its performance. The calibration methods are described, along with the results of Monte Carlo simulations of the telescope and comparisons between real and simulated data. The analysis of TeV $\gamma$-ray observations of the Crab Nebula, including the reconstructed energy spectrum, is shown to give results consistent with earlier measurements. The telescope is operating as expected and has met or exceeded all design specifications.Comment: Accepted by Astroparticle Physic

Development of the Bankruptcy Institution in Russia: Features of Procedural and Legal Regulation

The study of the development of bankruptcy institution procedural and legal regulation is very pressing in modern society, since the number of insolvent subjects is increasing every year, which inevitably increases the use of the norms of the institution being studied. However, in law enforcement practice, a number of problems arise due to the lack of a unified theoretical-based approach in constructing the legal regulation of the bankruptcy institution. The purpose of this study is to analyze the features of the procedural and legal regulation of the bankruptcy institution. The objectives of the study are to examine the system of legislation governing the bankruptcy institution, to analyze the law enforcement practice of declaring debtors insolvent, identifying problems of procedural regulation and the formulation of proposals for their elimination. In carrying out the study as the main method of knowledge, the authors relied on the materialist dialectic. In addition, other research methods were used: analysis and synthesis; induction, deduction; comparative law, etc. Abstracting from specific criteria and categorical problems, the study examined general provisions, concepts and categories of the institution of insolvency (bankruptcy), features of its procedural and legal regulation, as well as identified its problems. Due to a comprehensive and consistent analysis in accordance with the purpose and objectives of the study, which are its stages, it was possible to come to some conclusions and formulate certain recommendations. The significance of the study has both a theoretical aspect and an applied one: the formed theoretical concept of the institution of bankruptcy can enrich legal science, and proposals designed to solve existing law-enforcement problems can be used in the implementation of the norms of the institution under study

Large-space shell-model calculations for light nuclei

An effective two-body interaction is constructed from a new Reid-like $NN$ potential for a large no-core space consisting of six major shells and is used to generate the shell-model properties for light nuclei from $A$=2 to 6. (For practical reasons, the model space is partially truncated for $A$=6.) Binding energies and other physical observables are calculated and compare favorably with experiment.Comment: prepared using LaTex, 21 manuscript pages, no figure

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

GLRB allelic variation associated with agoraphobic cognitions, increased startle response and fear network activation : a potential neurogenetic pathway to panic disorder

The molecular genetics of panic disorder (PD) with and without agoraphobia (AG) are still largely unknown and progress is hampered by small sample sizes. We therefore performed a genome-wide association study with a dimensional, PD/AG - related anxiety phenotype based on the Agoraphobia Cognition Questionnaire (ACQ) in a sample of 1,370 healthy German volunteers of the CRC TRR58 MEGA study wave 1. A genome-wide significant association was found between ACQ and single non-coding nucleotide variants of the GLRB gene (rs78726293, p=3.3x10-8; rs191260602, p=3.9x10-8). We followed up on this finding in a larger dimensional ACQ sample (N=2,547) and in independent samples with a dichotomous AG phenotype based on the Symptoms Checklist (SCL-90; N=3,845) and a case control sample with the categorical phenotype PD/AG (Ncombined =1,012) obtaining highly significant p-values also for GLRB single nucleotide variants rs17035816 (p=3.8x10-4) and rs7688285 (p=7.6x10-5). GLRB gene expression was found to be modulated by rs7688285 in brain tissue as well as cell culture. Analyses of intermediate PD/AG phenotypes demonstrated increased startle reflex and increased fear network as well as general sensory activation by GLRB risk gene variants rs78726293, rs191260602, rs17035816 and rs7688285. Partial Glrb knockout-mice demonstrated an agoraphobic phenotype. In conjunction withthe clinical observation that rare coding GLRB gene mutations are associated with the neurological disorder hyperekplexia characterized by a generalized startle reaction and agoraphobic behavior, our data provide evidence that non-coding, though functional GLRB gene polymorphisms may predispose to PD by increasing startle response and agoraphobic cognitions.PostprintPeer reviewe