An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential

The potential -x^4, which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT-symmetric rather than Hermitian. Nonetheless it has been shown numerically to have a real spectrum, and a proof of reality, involving the correspondence between ordinary differential equations and integral systems, was subsequently constructed for the general class of potentials -(ix)^N. For PT-symmetric but non-Hermitian Hamiltonians the natural PT metric is not positive definite, but a dynamically-defined positive-definite metric can be defined, depending on an operator Q. Further, with the help of this operator an equivalent Hermitian Hamiltonian h can be constructed. This programme has been carried out exactly for a few soluble models, and the first few terms of a perturbative expansion have been found for the potential m^2x^2+igx^3. However, until now, the -x^4 potential has proved intractable. In the present paper we give explicit, closed-form expressions for Q and h, which are made possible by a particular parametrization of the contour in the complex plane on which the problem is defined. This constitutes an explicit proof of the reality of the spectrum. The resulting equivalent Hamiltonian has a potential with a positive quartic term together with a linear term.Comment: New reference [10] added and discussed. Minor typographical correction

On the Path-Integral Derivation of the Anomaly for the Hermitian Equivalent of the Complex PTPT-Symmetric Quartic Hamiltonian

It can be shown using operator techniques that the non-Hermitian $PT$-symmetric quantum mechanical Hamiltonian with a "wrong-sign" quartic potential $-gx^4$ is equivalent to a Hermitian Hamiltonian with a positive quartic potential together with a linear term. A naive derivation of the same result in the path-integral approach misses this linear term. In a recent paper by Bender et al. it was pointed out that this term was in the nature of a parity anomaly and a more careful, discretized treatment of the path integral appeared to reproduce it successfully. However, on re-examination of this derivation we find that a yet more careful treatment is necessary, keeping terms that were ignored in that paper. An alternative, much simpler derivation is given using the additional potential that has been shown to appear whenever a change of variables to curvilinear coordinates is made in a functional integral.Comment: LaTeX, 12 pages, no figure

Quiste gaseoso intrarraquídeo lumbar con síndrome radicular asociado: aportación de cuatro casos

Los autores aportan cuatro casos de síndrome radicular secundarios a una compresión radicular por quiste gaseosos intrarraquídeo extradural. El método de diagnóstico ha sido exploración con TAC y con RM. La presencia de gas intrarraquídeo es discutido en la bibliografía revisada.The authors describe four cases of secondary radicular syndrome due to radicular compression by a gas-containing cyst in the extradural space. The diagnosis was made by CT-Scan and MR imaging. The pathogenesis of the presence of epidural gas is discussed in the literature reviewed

Ca impurity in small mixed 4^4He-3^3He clusters

The structure of small mixed helium clusters doped with one calcium atom has been determined within the diffusion Monte Carlo framework. The results show that the calcium atom sits at the $^4$He-$^3$He interface. This is in agreement with previous studies, both experimental and theoretical, performed for large clusters. A comparison between the results obtained for the largest cluster we have considered for each isotope shows a clear tendency of the Ca atom to reside in a deep dimple at the surface of the cluster for $^4$He clusters, and to become fully solvated for $^3$He clusters. We have calculated the absorption spectrum of Ca around the $4s4p \leftarrow 4s^2$ transition and have found that it is blue-shifted from that of the free-atom transition by an amount that depends on the size and composition of the cluster.Comment: 24 pages, 11 figures. Accepted on Journal of Chemical Physic

Desorption Dynamics of Heavy Alkali Metal Atoms (Rb, Cs) off the Surface of Helium Nanodroplets

We present a combined ion imaging and density functional theory study of the dynamics of the desorption process of rubidium and cesium atoms off the surface of helium nanodroplets upon excitation of the perturbed $6s$ and $7s$ states, respectively. Both experimental and theoretical results are well represented by the pseudodiatomic model for effective masses of the helium droplet in the desorption reaction of m_eff/m_He~10 (Rb) and 13 (Cs). Deviations from this model are found for Rb excited to the 6p state. Photoelectron spectra indicate that the dopant-droplet interaction induces relaxation into low-lying electronic states of the desorbed atoms in the course of the ejection process.Comment: in press, J. Phys. Chem. A (2014

HST Studies of the WLM Galaxy. I. The Age and Metallicity of the Globular Cluster

We have obtained V and I images of the lone globular cluster that belongs to the dwarf Local Group irregular galaxy known as WLM. The color-magnitude diagram of the cluster shows that it is a normal old globular cluster with a well-defined giant branch reaching to M_V=-2.5, a horizontal branch at M_V=+0.5, and a sub-giant branch extending to our photometry limit of M_V=+2.0. A best fit to theoretical isochrones indicates that this cluster has a metallicity of [Fe/H]=-1.52\pm0.08 and an age of 14.8\pm0.6 Gyr, thus indicating that it is similar to normal old halo globulars in our Galaxy. From the fit we also find that the distance modulus of the cluster is 24.73\pm0.07 and the extinction is A_V=0.07\pm0.06, both values that agree within the errors with data obtained for the galaxy itself by others. We conclude that this normal massive cluster was able to form during the formation of WLM, despite the parent galaxy's very small intrinsic mass and size.Comment: 14 pages, 5 figures, 1 tabl

Effects of exoplanetary gravity on human locomotor ability

At some point in the future, if mankind hopes to settle planets outside the Solar System, it will be crucial to determine the range of planetary conditions under which human beings could survive and function. In this article, we apply physical considerations to future exoplanetary biology to determine the limitations which gravity imposes on several systems governing the human body. Initially, we examine the ultimate limits at which the human skeleton breaks and muscles become unable to lift the body from the ground. We also produce a new model for the energetic expenditure of walking, by modelling the leg as an inverted pendulum. Both approaches conclude that, with rigorous training, humans could perform normal locomotion at gravity no higher than 4 $g_{\textrm{Earth}}$.Comment: 12 pages, 4 figures, to be published in The Physics Teache

Variable stars in the Fornax dSph Galaxy. II. Pulsating stars below the horizontal branch

We have carried out an intensive survey of the northern region of the Fornax dwarf spheroidal galaxy with the aim of detecting the galaxy's short--period pulsating stars (P<0.25 days). Observations collected over three consecutive nights with the Wide Field Imager of the 2.2m MPI telescope at ESO allowed us to detect 85 high-amplitude (0.20-1.00 mag in B-light) variable stars with periods in the range from 0.046 to 0.126 days, similar to SX Phoenicis stars in Galactic metal-poor stellar populations. The plots of the observed periods vs. the B and V magnitudes show a dispersion largely exceeding the observational errors. To disentangle the matter, we separated the first-overtone from the fundamental-mode pulsators and tentatively identified a group of subluminous variables, about 0.35 mag fainter than the others. Their nature as either metal-poor intermediate-age stars or stars formed by the merging of close binary systems is discussed. The rich sample of the Fornax variables also led us to reconstruct the Period-Luminosity relation for short-period pulsating stars. An excellent linear fit, M(V)=-1.83(+/-0.08)-3.65(+/-0.07) log P(fund), was obtained using 153 Delta Scuti and SX Phoenicis stars in a number of different stellar systems.Comment: 11 pages plus 1 on-line figure and 1 on-line table; accepted for publication in ApJ. Part of this work has been the subject of the Laurea thesis of LDA. His supervisor and our colleague, Prof. Laura E. Pasinetti, suddendly passed away on September 13, 2006. Several astronomers have been trained under her tutelage and we gratefully honor her memor

The Case Against Cosmology

It is argued that some of the recent claims for cosmology are grossly overblown. Cosmology rests on a very small database: it suffers from many fundamental difficulties as a science (if it is a science at all) whilst observations of distant phenomena are difficult to make and harder to interpret. It is suggested that cosmological inferences should be tentatively made and sceptically received.Comment: 9 pages, no figure