Scattering in the PT-symmetric Coulomb potential

Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary conditions for bound states and also allows the restoration of the correct sign of the energy eigenvalues. Scattering states are composed from the two linearly independent solutions valid for non-integer values of the 2L parameter, which would correspond to the angular momentum in the usual Hermitian setting. Transmission and reflection coefficients are written in closed analytic form and it is shown that similarly to other ${\cal PT}$-symmetric scattering systems the latter exhibit handedness effect. Bound-state energies are recovered from the poles of the transmission coefficients.Comment: Journal of Physics A: Mathematical and Theoretical 42 (2009) to appea

Solvent response to fluorine-atom reaction dynamics in liquid acetonitrile

Solvent restructuring and vibrational cooling follow exothermic fluorine-atom reactions in acetonitrile.</p

Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach

We have applied the momentum space version of the Density Matrix Renormalization Group method ($k$-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in the new context. We have shown numerically that it is possible to determine the desired accuracy of the method in advance of the calculations by dynamically controlling the truncation error and the number of block states using a novel protocol which we dubbed Dynamical Block State Selection (DBSS). The relationship between the real error and truncation error has been studied as a function of the number of orbitals and the fraction of filled orbitals. We have calculated the ground state of the molecules CH$_2$, H$_2$O, and F$_2$ as well as the first excited state of CH$_2$. Our largest calculations were carried out with 57 orbitals, the largest number of block states was 1500--2000, and the largest dimensions of the Hilbert space of the superblock configuration was 800.000--1.200.000.Comment: 12 page

The cost of reducing starting RNA quantity for Illumina BeadArrays: a bead-level dilution experiment.

BACKGROUND: The demands of microarray expression technologies for quantities of RNA place a limit on the questions they can address. As a consequence, the RNA requirements have reduced over time as technologies have improved. In this paper we investigate the costs of reducing the starting quantity of RNA for the Illumina BeadArray platform. This we do via a dilution data set generated from two reference RNA sources that have become the standard for investigations into microarray and sequencing technologies. RESULTS: We find that the starting quantity of RNA has an effect on observed intensities despite the fact that the quantity of cRNA being hybridized remains constant. We see a loss of sensitivity when using lower quantities of RNA, but no great rise in the false positive rate. Even with 10 ng of starting RNA, the positive results are reliable although many differentially expressed genes are missed. We see that there is some scope for combining data from samples that have contributed differing quantities of RNA, but note also that sample sizes should increase to compensate for the loss of signal-to-noise when using low quantities of starting RNA. CONCLUSIONS: The BeadArray platform maintains a low false discovery rate even when small amounts of starting RNA are used. In contrast, the sensitivity of the platform drops off noticeably over the same range. Thus, those conducting experiments should not opt for low quantities of starting RNA without consideration of the costs of doing so. The implications for experimental design, and the integration of data from different starting quantities, are complex.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Identification of observables in quantum toboggans

Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of states. The recipe is extended here to quantum toboggans. In the first step the tobogganic integration path is rectified and the Schroedinger equation is given the generalized eigenvalue-problem form. In the second step the general double-series representation of the eligible metric operators is derived.Comment: 25 p

Revenue divergence and competitive balance in a divisional sports league

The North American model of resource allocation in professional sports leagues is adapted for English (association) football. The theoretical relationship between revenue and competitive balance is shown to be robust with respect to changes in teams’ objectives and labour market conditions. Empirical revenue functions are reported for 1926-1999. These indicate a shift in the composition of demand favouring big-city teams and an increase in the sensitivity of revenue to performance. An analysis of match results in the FA Cup competition suggests an increase in competitive imbalance between teams at different levels of the league’s divisional hierarchy, as the theory suggests

Phase transitions with finite atom number in the Dicke Model

Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are the number of photons inside the cavity and the number of excited atoms. Coherent states provide a mean field description, which becomes exact in the thermodynamic limit. Employing symmetry adapted (SA) SU(2) coherent states (SACS) the critical behavior can be described for a finite number of atoms. A variation after projection treatment, involving a numerical minimization of the SA energy surface, associates the finite number phase transition with a discontinuity in the order parameters, which originates from a competition between two local minima in the SA energy surface.Comment: 8 pages, 10 figures, Conference Proceedings of CEWQO-2012, to be published as a Topical Issue of the journal Physica Script

How a firm's domestic footprint and domestic environmental uncertainties jointly shape added cultural distances : the roles of resource dependence and headquarters attention

Even though many firms conduct most of their business domestically, international management research has remained remarkably silent on the role of a firm's domestic footprint in its internationalization strategy. We shed light on that role by exploring how the size of a firm's domestic footprint influences the cultural distance that the firm adds to its country portfolio when expanding internationally. Integrating resource dependence theory and the attention‐based view, we hypothesize that a firm's domestic footprint has a negative relationship with added cultural distance (ACD), and that domestic policy uncertainty strengthens this relationship whereas domestic demand uncertainty weakens it. We find robust support for our hypotheses in a sample of the world's largest retailers covering the period 2000–07, indicating that a firm's domestic footprint and domestic environmental uncertainties jointly shape cross‐cultural expansion strategies. Our findings suggest that ACDs reflect headquarters executives' desire to avoid ineffective foreign expansions, hinting at possible biases in studies of the performance effects of distance

Influence of electron correlations on ground-state properties of III-V semiconductors

Lattice constants and bulk moduli of eleven cubic III-V semiconductors are calculated using an ab initio scheme. Correlation contributions of the valence electrons, in particular, are determined using increments for localized bonds and for pairs and triples of such bonds; individual increments, in turn, are evaluated using the coupled cluster approach with single and double excitations. Core-valence correlation is taken into account by means of a core polarization potential. Combining the results at the correlated level with corresponding Hartree-Fock data, we obtain lattice constants which agree with experiment within an average error of -0.2%; bulk moduli are accurate to +4%. We discuss in detail the influence of the various correlation contributions on lattice constants and bulk moduli.Comment: 4 pages, Latex, no figures, Phys. Rev. B, accepte

Characterization of the Photo-emf Response for Laser-Based Ultrasonic Sensing Under Simulated Industrial Conditions

There is a need in myriad manufacturing environments to nondestructively evaluate components and to control processes in real-time. Laser-based ultrasound [1,2], LBU, has the potential to be a robust, reconfigurable, noncontact diagnostic for many industrial applications. A simple and inexpensive semiconductor sensor based on the nonsteady-state photo-induced-electromotive force (photo-emf) effect [3,4], has been demonstrated [5] to be functional under a variety of manufacturing conditions and in probing various materials, including metals, semiconductors, and organics. This device has the potential to remotely sense ultrasound via speckle motion or coherent detection over a reasonable field-of-view, with good bandwidth and detection sensitivity. In addition, the detector can, at the same time, compensate for otherwise deleterious static and dynamic environmental distortions in real-time, including speckle, beam wander, poor-quality optics, and propagation distortions over free-space paths and through multi-mode optical fibers. Such inspection tools can improve the efficiency, yield and performance of various manufacturing processes, including bonds, surface treatments, case hardening, composites, metallurgy, microcrack detection, adhesion, remote temperature and thickness measurements. By performing the inspection on-line and in real-time, the possibility exists for closed-loop, in-process control. This can lead to reduced cost, labor, scrap, and machine downtime in today’s highly competitive markets