Zero-energy states in graphene quantum dots and rings

We present exact analytical zero-energy solutions for a class of smooth decaying potentials, showing that the full confinement of charge carriers in electrostatic potentials in graphene quantum dots and rings is indeed possible without recourse to magnetic fields. These exact solutions allow us to draw conclusions on the general requirements for the potential to support fully confined states, including a critical value of the potential strength and spatial extent.Comment: 8 pages, 3 figures, references added, typos corrected, discussion section expande

Family health narratives : midlife women’s concepts of vulnerability to illness

Perceptions of vulnerability to illness are strongly influenced by the salience given to personal experience of illness in the family. This article proposes that this salience is created through autobiographical narrative, both as individual life story and collectively shaped family history. The paper focuses on responses related to health in the family drawn from semi-structured interviews with women in a qualitative study exploring midlife women’s health. Uncertainty about the future was a major emergent theme. Most respondents were worried about a specified condition such as heart disease or breast cancer. Many women were uncertain about whether illness in the family was inherited. Some felt certain that illness in the family meant that they were more vulnerable to illness or that their relatives’ ageing would be mirrored in their own inevitable decline, while a few expressed cautious optimism about the future. In order to elucidate these responses, we focused on narratives in which family members’ appearance was discussed and compared to that of others in the family. The visualisation of both kinship and the effects of illness, led to strong similarities being seen as grounds for worry. This led to some women distancing themselves from the legacies of illness in their families. Women tended to look at the whole family as the context for their perceptions of vulnerability, developing complex patterns of resemblance or difference within their families

The double well potential in quantum mechanics: a simple, numerically exact formulation

The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important in quantum information theory. It is therefore desirable to have solutions to simple double well potentials that are accessible to the undergraduate student. We describe a method for obtaining the numerically exact eigenenergies and eigenstates for such a model, along with the energies obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact solution is accessible with elementary mathematics, though numerical solutions are required. We also find that the WKB approximation is remarkably accurate, not just for the ground state, but for the excited states as well.Comment: 10 pages, 4 figures; suitable for undergraduate courses in quantum mechanic

Comparing periodic-orbit theory to perturbation theory in the asymmetric infinite square well

An infinite square well with a discontinuous step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits in the semiclassical limit. This system is analyzed using both time-independent perturbation theory (PT) and periodic-orbit theory and the approximate formulas for the energy eigenvalues derived from these two approaches are compared. The periodic orbits of the system can be divided into classes according to how many times they reflect from the potential step. Different classes of orbits contribute to different orders of PT. The dominant term in the second-order PT correction is due to non-Newtonian orbits that reflect from the step exactly once. In the limit in which PT converges the periodic-orbit theory results agree with those of PT, but outside of this limit the periodic-orbit theory gives much more accurate results for energies above the potential step.Comment: 22 pages, 2 figures, 2 tables, submitted to Physical Review

An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains

Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution of a Heisenberg spin-1/2 chain and interpreting the results based on the analysis of the eigenvalues, eigenstates, and symmetries of the system. We make available online all computer codes used to obtain our data.Comment: 8 pages, 3 figure

P,T-Violating Nuclear Matrix Elements in the One-Meson Exchange Approximation

Expressions for the P,T-violating NN potentials are derived for $\pi$, $\rho$ and $\omega$ exchange. The nuclear matrix elements for $\rho$ and $\omega$ exchange are shown to be greatly suppressed, so that, under the assumption of comparable coupling constants, $\pi$ exchange would dominate by two orders of magnitude. The ratio of P,T-violating to P-violating matrix elements is found to remain approximately constant across the nuclear mass table, thus establishing the proportionality between time-reversal-violation and parity-violation matrix elements. The calculated values of this ratio suggest a need to obtain an accuracy of order $5 \times 10^{-4}$ for the ratio of the PT-violating to P-violating asymmetries in neutron transmission experiments in order to improve on the present limits on the isovector pion coupling constant.Comment: 17 pages, LaTeX, no figure

Symbolic Manipulators Affect Mathematical Mindsets

Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work

Exploring a rheonomic system

A simple and illustrative rheonomic system is explored in the Lagrangian formalism. The difference between Jacobi's integral and energy is highlighted. A sharp contrast with remarks found in the literature is pointed out. The non-conservative system possess a Lagrangian not explicitly dependent on time and consequently there is a Jacobi's integral. The Lagrange undetermined multiplier method is used as a complement to obtain a few interesting conclusion

Complex temperatures zeroes of partition function in spin-glass models

An approximate method is proposed for investigating complex-temperature properties of real-dimensional spin-glass models. The method uses the complex-temperature data of the ferromagnetic model on the same lattice. The universality line in the complex-temperature space is obtained.Comment: latex, corrected some misprint

Free radical reactions in atherosclerosis; An EPR spectrometry study

The copper catalysed oxidation of homocysteine has been studied by electron paramagnetic resonance (EPR) spectroscopy and spin trapping techniques to determine the nature of free radical species formed under varying experimental conditions. Three radicals; thiyl, alkyl and hydroxyl were detected with hydroxyl being predominant. A reaction mechanism is proposed involving Fenton chemistry. Inclusion of catalase to test for intermediate generation of hydrogen peroxide showed a marked reduction in amount of hydroxyl radical generated. In contrast, the addition of superoxide dismutase showed no significant effect on the level of hydroxyl radical formed. Enhanced radical formation was observed at higher levels of oxygen, an effect which has consequences for differential oxygen levels in arterial and venous systems. Implications are drawn for a higher incidence of atherosclerotic plaque formation in arteries versus veins. © 2006 - IOS Press and the authors. All rights reserved