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.

Financial Inclusion: Lessons From Rural South India

Financial inclusion/exclusion has recently been emphasised as an important policy option aimed at alleviating poverty, minimising social exclusion and enhancing economic growth. In this article, we review the growing interest in financial exclusion and inclusion, define them and demonstrate their existence in developing and developed countries. Our empirical focus is on whether financial inclusion has been successfully implemented in four sites in rural South India where banks claimed that financial inclusion is complete. Although many rural people in South India are financially included, the concept of financial inclusion is more complex than usually portrayed. Our findings show that social and personal deprivation contributes to financial exclusion and should be viewed as key barriers to financial inclusion. We also suggest that financial inclusion is not a monolithic phenomenon and should be studied in a multi-layered fashion, ranging from having a bank account to making full use of modern financial instruments

Distributed leadership, trust and online communities

This paper analyses the role of distributed leadership and trust in online communities. The team-based informal ethos of online collaboration requires a different kind of leadership from that in formal positional hierarchies. Such leadership may be more flexible and sophisticated, capable of encompassing ambiguity and rapid change. Online leaders need to be partially invisible, delegating power and distributing tasks. Yet, simultaneously, online communities are facilitated by the high visibility and subtle control of expert leaders. This paradox: that leaders need to be both highly visible and invisible as appropriate, was derived from prior research and tested in the analysis of online community discussions using a pattern-matching process. It is argued that both leader visibility and invisibility are important for the facilitation of trusting collaboration via distributed leadership. Advanced leadership responses to complex situations in online communities foster positive group interaction and decision-making, facilitated through active distribution of specific tasks

Access to recreational physical activities by car and bus : an assessment of socio-spatial inequalities in mainland Scotland

Obesity and other chronic conditions linked with low levels of physical activity (PA) are associated with deprivation. One reason for this could be that it is more difficult for low-income groups to access recreational PA facilities such as swimming pools and sports centres than high-income groups. In this paper, we explore the distribution of access to PA facilities by car and bus across mainland Scotland by income deprivation at datazone level. GIS car and bus networks were created to determine the number of PA facilities accessible within travel times of 10, 20 and 30 minutes. Multilevel negative binomial regression models were then used to investigate the distribution of the number of accessible facilities, adjusting for datazone population size and local authority. Access to PA facilities by car was significantly (p<0.01) higher for the most affluent quintile of area-based income deprivation than for most other quintiles in small towns and all other quintiles in rural areas. Accessibility by bus was significantly lower for the most affluent quintile than for other quintiles in urban areas and small towns, but not in rural areas. Overall, we found that the most disadvantaged groups were those without access to a car and living in the most affluent areas or in rural areas

Small-scale flows in SUMER and TRACE high-cadence co-observations

We report on the physical properties of small-scale transient flows observed simultaneously at high cadence with the SUMER spectrometer and the TRACE imager in the plage area of an active region. Our major objective is to provide a better understanding of the nature of transient phenomena in the solar atmosphere by using high-cadence imager and spectrometer co-observations at similar spatial and temporal resolution. A sequence of TRACE Fe IX/X 171 A and high-resolution MDI images were analysed together with simultaneously obtained SUMER observations in spectral lines covering a temperature range from 10 000 K to 1 MK. We reveal the existence of numerous transient flows in small-scale loops (up to 30 Mm) observed in the plage area of an active region. These flows have temperatures from 10 000 K (the low temperature limit of our observations) to 250 000 K. The coronal response of these features is uncertain due to a blending of the observed coronal line Mg X 624.85 A. The duration of the events ranges from 60 s to 19 min depending on the loop size. Some of the flows reach supersonic velocities. The Doppler shifts often associated with explosive events or bi-directional jets can actually be identified with flows (some of them reaching supersonic velocities) in small-scale loops. Additionally, we demonstrate how a line-of-sight effect can give misleading information on the nature of the observed phenomena if only either an imager or a spectrometer is used.Comment: 7 pages, 6 figures, accepted by A&

Inelastic Quantum Transport

We solve a Schrodinger equation for inelastic quantum transport that retains full quantum coherence, in contrast to previous rate or Boltzmann equation approaches. The model Hamiltonian is the zero temperature 1d Holstein model for an electron coupled to optical phonons (polaron), in a strong electric field. The Hilbert space grows exponentially with electron position, forming a non-standard Bethe lattice. We calculate nonperturbatively the transport current, electron-phonon correlations, and quantum diffusion. This system is a toy model for the constantly branching ``wavefunction of the universe''.Comment: revtex, 13 pages, 4 figure

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

Interictal Neurocognitive Processing of Visual Stimuli in Migraine: Evidence from Event-Related Potentials

Research has established decreased sensory habituation as a defining feature in migraine, while decreased cognitive habituation has only been found with regard to cognitive assessment of the relative probability of the occurrence of a stimulus event. Our study extended the investigation of interictal habituation in migraine to include cognitive processing when viewing of a series of visually-complex images, similar to those we encounter on the internet everyday. We examined interictal neurocognitive function in migraine from a habituation perspective, using a novel paradigm designed to assess how the response to a series of images changes over time. Two groups of participants--migraineurs (N = 25) and non-migraine controls (N = 25)--were asked to view a set of 232 unfamiliar logos in the context of a target identification task as their brain electrical responses were recorded via event-related potentials (ERPs). The set of logos was viewed serially in each of 10 separate trial blocks, with data analysis focusing on how the ERP responses to the logos in frontal electrodes from 200-600 ms changed across time within each group. For the controls, we found that the amplitude of the late positive potential (LPP) ERP component elicited by the logos had no significant change across trial blocks. In contrast, in migraineurs we found that the LPP significantly increased in amplitude across trial blocks, an effect consistent with a lack of habituation to visual stimuli seen in previous research. Our findings provide empirical support abnormal cognitive processing of complex visual images across time in migraineurs that goes beyond the sensory-level habituation found in previous research

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

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