Generating Bounds for the Ground State Energy of the Infinite Quantum Lens Potential

Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converging lower and upper bounds to a specific discrete state energy, once the signature property of the associated wavefunction is known. This method is particularly effective for multidimensional, bosonic ground state problems, since the corresponding wavefunction must be of uniform signature, and can be taken to be positive. Despite this, the vast majority of problems studied have been on unbounded domains. The important problem of an electron in an infinite quantum lens potential defines a challenging extension of EMM to systems defined on a compact domain. We investigate this here, and introduce novel modifications to the conventional EMM formalism that facilitate its adaptability to the required boundary conditions.Comment: Submitted to J. Phys.

Benchmark full configuration-interaction calculations on HF and NH2

Full configuration-interaction (FCI) calculations are performed at selected geometries for the 1-sigma(+) state of HF and the 2-B(1) and 2-A(1) states of NH2 using both DZ and DZP gaussian basis sets. Higher excitations become more important when the bonds are stretched and the self-consistent field (SCF) reference becomes a poorer zeroth-order description of the wave function. The complete active space SCF - multireference configuration-interaction (CASSCF-MRCI) procedure gives excellent agreement with the FCI potentials, especially when corrected with a multi-reference analog of the Davidson correction

Space of State Vectors in PT Symmetrical Quantum Mechanics

Space of states of PT symmetrical quantum mechanics is examined. Requirement that eigenstates with different eigenvalues must be orthogonal leads to the conclusion that eigenfunctions belong to the space with an indefinite metric. The self consistent expressions for the probability amplitude and average value of operator are suggested. Further specification of space of state vectors yield the superselection rule, redefining notion of the superposition principle. The expression for the probability current density, satisfying equation of continuity and vanishing for the bound state, is proposed.Comment: Revised version, explicit expressions for average values and probability amplitude adde

Effect of electron exchange on atomic ionization in a strong electric field

Hartree-Fock atom in a strong electric static field is considered. It is demonstrated that exchange between outer and inner electrons, taken into account by the so-called Fock term affects strongly the long-range behavior of the inner electron wave function. As a result, it dramatically increases its probability to be ionized. A simple model is analyzed demonstrating that the decay probability, compared to the case of a local (Hartree) atomic potential, increases by many orders of magnitude. As a result of such increase, the ratio of inner to outer electrons ionization probability became not too small. It is essential that the effect of exchange upon probability of inner electron ionization by strong electric field is proportional to the square of the number of outer electrons. It signals that in clusters the inner electron ionization by strong field, the very fact of which is manifested by e.g. high energy quanta emission, has to be essentially increased as compared to this process in gaseous atomic objects.Comment: 7 pages, 1 figur

Study of a class of non-polynomial oscillator potentials

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.Comment: 16 page

Two-Dimensional Spectroscopy of Photospheric Shear Flows in a Small delta Spot

In recent high-resolution observations of complex active regions, long-lasting and well-defined regions of strong flows were identified in major flares and associated with bright kernels of visible, near-infrared, and X-ray radiation. These flows, which occurred in the proximity of the magnetic neutral line, significantly contributed to the generation of magnetic shear. Signatures of these shear flows are strongly curved penumbral filaments, which are almost tangential to sunspot umbrae rather than exhibiting the typical radial filamentary structure. Solar active region NOAA 10756 was a moderately complex, beta-delta sunspot group, which provided an opportunity to extend previous studies of such shear flows to quieter settings. We conclude that shear flows are a common phenomenon in complex active regions and delta spots. However, they are not necessarily a prerequisite condition for flaring. Indeed, in the present observations, the photospheric shear flows along the magnetic neutral line are not related to any change of the local magnetic shear. We present high-resolution observations of NOAA 10756 obtained with the 65-cm vacuum reflector at Big Bear Solar Observatory (BBSO). Time series of speckle-reconstructed white-light images and two-dimensional spectroscopic data were combined to study the temporal evolution of the three-dimensional vector flow field in the beta-delta sunspot group. An hour-long data set of consistent high quality was obtained, which had a cadence of better than 30 seconds and sub-arcsecond spatial resolution.Comment: 23 pages, 6 gray-scale figures, 4 color figures, 2 tables, submitted to Solar Physic

Trust and control interrelations: New perspectives on the trust control nexus

This article is the post-print version of the published article that may be accessed at the link below. Copyright @ 2007 Sage Publications.This article introduces the special issue on New Perspectives on the Trust-Control Nexus in Organizational Relations. Trust and control are interlinked processes commonly seen as key to reach effectiveness in inter- and intraorganizational relations. The relation between trust and control is, however, a complex one, and research into this relation has given rise to various and contradictory interpretations of how trust and control relate. A well-known discussion is directed at whether trust and control are better conceived as substitutes, or as complementary mechanisms of governance. The articles in this special issue bring the discussion on the relationship between both concepts a step further by identifying common factors, distinctive mechanisms, and key implications relevant for theory building and empirical research. By studying trust and control through different perspectives and at different levels of analysis, the articles provide new theoretical insights and empirical evidence on the foundations of the trust-control interrelations

Solvable simulation of a double-well problem in PT symmetric quantum mechanics

Within quantum mechanics which works with parity-pseudo-Hermitian Hamiltonians we study the tunneling in a symmetric double well formed by two delta functions with complex conjugate strengths. The model is exactly solvable and exhibits several interesting features. Besides an amazingly robust absence of any PT symmetry breaking, we observe a quasi-degeneracy of the levels which occurs all over the energy range including the high-energy domain. This pattern is interpreted as a manifestation of certain "quantum beats".Comment: 12 pages incl. 7 figure

Multiwavelength Study on Solar and Interplanetary Origins of the Strongest Geomagnetic Storm of Solar Cycle 23

We study the solar sources of an intense geomagnetic storm of solar cycle 23 that occurred on 20 November 2003, based on ground- and space-based multiwavelength observations. The coronal mass ejections (CMEs) responsible for the above geomagnetic storm originated from the super-active region NOAA 10501. We investigate the H-alpha observations of the flare events made with a 15 cm solar tower telescope at ARIES, Nainital, India. The propagation characteristics of the CMEs have been derived from the three-dimensional images of the solar wind (i.e., density and speed) obtained from the interplanetary scintillation data, supplemented with other ground- and space-based measurements. The TRACE, SXI and H-alpha observations revealed two successive ejections (of speeds ~350 and ~100 km/s), originating from the same filament channel, which were associated with two high speed CMEs (~1223 and ~1660 km/s, respectively). These two ejections generated propagating fast shock waves (i.e., fast drifting type II radio bursts) in the corona. The interaction of these CMEs along the Sun-Earth line has led to the severity of the storm. According to our investigation, the interplanetary medium consisted of two merging magnetic clouds (MCs) that preserved their identity during their propagation. These magnetic clouds made the interplanetary magnetic field (IMF) southward for a long time, which reconnected with the geomagnetic field, resulting the super-storm (Dst_peak=-472 nT) on the Earth.Comment: 24 pages, 16 figures, Accepted for publication in Solar Physic

Leadership, the logic of sufficiency and the sustainability of education

The notion of sufficiency has not yet entered mainstream educational thinking, and it still has to make its mark upon educational leadership. However, a number of related concepts – particularly those of sustainability and complexity theory – are beginning to be noticed. This article examines these two concepts and uses them to critique the quasi-economic notion of efficiency, before arguing that the concept of sufficiency arises naturally from this discussion. This concept, originally derived from environmental thinking, has both metaphorical and practical impact for educational organizations and their leadership. An examination of three possible meanings suggests that while an embrace of an imperative concept of sufficiency seems increasingly necessary, its adoption would probably lead to a number of other problems, as it challenges some fundamental societal values and assumptions. Nevertheless, the article argues that these need to be addressed for the sake of both sustainable leadership and a sustainable planet