PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics

In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x real. We will give a complete characterization of three different classes of operators associated with the differential expression H: The class of all self-adjoint (Hermitian) operators, the class of all PT symmetric operators and the class of all P-self-adjoint operators. Surprisingly, some of the PT symmetric operators associated to this expression have no resolvent set

Massive Dirac particles on the background of charged de-Sitter black hole manifolds

We consider the behavior of massive Dirac fields on the background of a charged de-Sitter black hole. All black hole geometries are taken into account, including the Reissner-Nordstr\"{o}m-de-Sitter one, the Nariai case and the ultracold case. Our focus is at first on the existence of bound quantum mechanical states for the Dirac Hamiltonian on the given backgrounds. In this respect, we show that in all cases no bound state is allowed, which amounts also to the non-existence of normalizable time-periodic solutions of the Dirac equation. This quantum result is in contrast to classical physics, and it is shown to hold true even for extremal cases. Furthermore, we shift our attention on the very interesting problem of the quantum discharge of the black holes. Following Damour-Deruelle-Ruffini approach, we show that the existence of level-crossing between positive and negative continuous energy states is a signal of the quantum instability leading to the discharge of the black hole, and in the cases of the Nariai geometry and of the ultracold geometries we also calculate in WKB approximation the transmission coefficient related to the discharge process.Comment: 19 pages, 11 figures. Macro package: Revtex4. Changes concern mainly the introduction and the final discussion in section VI; moreover, Appendix D on the evaluation of the Nariai transmission integral has been added. References adde

Spectroscopy of southern Galactic disk planetary nebulae. Notes on chemical composition and emission-line stars

We present low resolution spectroscopic observations for a sample of 53 planetary nebulae (PNe) located in the southern sky between Vela and Norma constellations and pertaining to the Galactic disk with expected Galactocentric distance range of 5 to 10 kpc. We derive nebular chemical composition and plasma parameters with the classical empirical method. For most of the observed objects, this has been done for the first time. The distributions of the chemical abundances of the observed disk sample are generally indistinguishable from Galactic bulge and inner-disk PNe populations. The exceptions are possible differences in the He/H distribution, as compared to bulge PNe and Ne/Ar, compared to inner-disk PNe sample. The derived O/H ratios for the observed disk PNe fit to the concept of flattening of the chemical gradient in the inner parts of the Milky Way. We use the spectra to search for emission-line central stars in the observed sample. We found 6 new emission-line central stars comprising examples of all known types: WEL, VL and [WR]. We confirm that these types represent three evolutionary unconnected forms of enhanced mass-loss in the central stars of PNe. We note on the problem of high ionisation PNe with nebular CIV emission that can mimic the presence of WEL central stars in 1D spectra.Comment: 35 pages, 19 figures, 4 tables (Note: corrected error in measured flux of [O II] 7325 lines in Table B.1

Evaluation of Aposphaeria amaranthi as a Bioherbicide for Pigweed (Amaranthus Spp.)

Studies were conducted to determine the potential of the fungus, Aposphaeria amaranth!, as a bioherbicide for pigweeds (Amaranthus spp.). Experiments to establish the environmental parameters necessary for control of tumble pigweed (A. albus) demonstrated that an 8-hr dew period was sufficient for control of seedlings with four to six leaves, and that temperatures ranging from 20 to 28 C were conducive for disease development. Conidial concentrations as lowas 1x 10s conidia per ml also were sufficient for plant mortality. Host range tests demonstrated pathogenicity of A. amaranthi to several other species of Amaranthus, including biotypes resistant to triazine herbicides. Disease on redroot pigweed (A. retroflexus) was enhanced by incorporation of surfactants into inoculum suspensions. Field tests conducted in 1990 resulted in 73% control of redroot pigweed and 99% control of tumble pigweed. These results suggest that Aposphaeria amaranthi has potential as a bioherbicide for controlling pigweeds

Properties of pedestrians walking in line: Stepping behavior

In human crowds, interactions among individuals give rise to a variety of self-organized collective motions that help the group to effectively solve the problem of coordination. However, it is still not known exactly how humans adjust their behavior locally, nor what are the direct consequences on the emergent organization. One of the underlying mechanisms of adjusting individual motions is the stepping dynamics. In this paper, we present first quantitative analysis on the stepping behavior in a one-dimensional pedestrian flow studied under controlled laboratory conditions. We find that the step length is proportional to the velocity of the pedestrian, and is directly related to the space available in front of him, while the variations of the step duration are much smaller. This is in contrast with locomotion studies performed on isolated pedestrians and shows that the local density has a direct influence on the stepping characteristics. Furthermore, we study the phenomena of synchronization -walking in lockstep- and show its dependence on flow densities. We show that the synchronization of steps is particularly important at high densities, which has direct impact on the studies of optimizing pedestrians flow in congested situations. However, small synchronization and antisynchronization effects are found also at very low densities, for which no steric constraints exist between successive pedestrians, showing the natural tendency to synchronize according to perceived visual signals.Comment: 8 pages, 5 figure

On the spectrum of a bent chain graph

We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever $\alpha\ne 0$. We consider a "bending" deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling $\alpha$ and the "bending angle" as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.Comment: LaTeX, 23 pages with 7 figures; minor changes, references added; to appear in J. Phys. A: Math. Theo

Electronic States of Graphene Grain Boundaries

We introduce a model for amorphous grain boundaries in graphene, and find that stable structures can exist along the boundary that are responsible for local density of states enhancements both at zero and finite (~0.5 eV) energies. Such zero energy peaks in particular were identified in STS measurements [J. \v{C}ervenka, M. I. Katsnelson, and C. F. J. Flipse, Nature Physics 5, 840 (2009)], but are not present in the simplest pentagon-heptagon dislocation array model [O. V. Yazyev and S. G. Louie, Physical Review B 81, 195420 (2010)]. We consider the low energy continuum theory of arrays of dislocations in graphene and show that it predicts localized zero energy states. Since the continuum theory is based on an idealized lattice scale physics it is a priori not literally applicable. However, we identify stable dislocation cores, different from the pentagon-heptagon pairs, that do carry zero energy states. These might be responsible for the enhanced magnetism seen experimentally at graphite grain boundaries.Comment: 10 pages, 4 figures, submitted to Physical Review

Asymptotic behaviour of the spectrum of a waveguide with distant perturbations

We consider the waveguide modelled by a $n$-dimensional infinite tube. The operator we study is the Dirichlet Laplacian perturbed by two distant perturbations. The perturbations are described by arbitrary abstract operators ''localized'' in a certain sense, and the distance between their ''supports'' tends to infinity. We study the asymptotic behaviour of the discrete spectrum of such system. The main results are a convergence theorem and the asymptotics expansions for the eigenvalues. The asymptotic behaviour of the associated eigenfunctions is described as well. We also provide some particular examples of the distant perturbations. The examples are the potential, second order differential operator, magnetic Schroedinger operator, curved and deformed waveguide, delta interaction, and integral operator

Discovery of a [WO] central star in the planetary nebula Th 2-A

% context About 2500 planetary nebulae are known in our Galaxy but only 224 have central stars with reported spectral types in the Strasbourg-ESO Catalogue of Galactic Planetary Nebulae (Acker et al. 1992; Acker et al. 1996) % aims We have started an observational program aiming to increase the number of PN central stars with spectral classification. % methods By means of spectroscopy and high resolution imaging, we identify the position and true nature of the central star. We carried out low resolution spectroscopic observations at CASLEO telescope, complemented with medium resolution spectroscopy performed at Gemini South and Magellan telescopes. % results As a first outcome of this survey, we present for the first time the spectra of the central star of the PN Th 2-A. These spectra show emission lines of ionized C and O, typical in Wolf-Rayet stars. % conclusions We identify the position of that central star, which is not the brightest one of the visual central pair. We classify it as of type [WO 3]pec, which is consistent with the high excitation and dynamical age of the nebula.Comment: 3 pages and 2 figures. Paper recommended for publication in A&

MenaINV dysregulates cortactin phosphorylation to promote invadopodium maturation

Invadopodia, actin-based protrusions of invasive carcinoma cells that focally activate extracellular matrix-degrading proteases, are essential for the migration and intravasation of tumor cells during dissemination from the primary tumor. We have previously shown that cortactin phosphorylation at tyrosine residues, in particular tyrosine 421, promotes actin polymerization at newly-forming invadopodia, promoting their maturation to matrix-degrading structures. However, the mechanism by which cells regulate the cortactin tyrosine phosphorylation-dephosphorylation cycle at invadopodia is unknown. Mena, an actin barbed-end capping protein antagonist, is expressed as various splice-isoforms. The MenaINV isoform is upregulated in migratory and invasive sub-populations of breast carcinoma cells, and is involved in tumor cell intravasation. Here we show that forced MenaINV expression increases invadopodium maturation to a far greater extent than equivalent expression of other Mena isoforms. MenaINV is recruited to invadopodium precursors just after their initial assembly at the plasma membrane, and promotes the phosphorylation of cortactin tyrosine 421 at invadopodia. In addition, we show that cortactin phosphorylation at tyrosine 421 is suppressed by the phosphatase PTP1B, and that PTP1B localization to the invadopodium is reduced by MenaINV expression. We conclude that MenaINV promotes invadopodium maturation by inhibiting normal dephosphorylation of cortactin at tyrosine 421 by the phosphatase PTP1B.United States. National Institutes of Health (CA150344)United States. National Institutes of Health (CA100324