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

Supersymmetry on Graphs and Networks

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral properties for a class of graph operators which typically encode relevant graph characteristics.Comment: 11 pages, Latex, no figures, remark 4.1 added, slight alterations in lemma 5.3, a more detailed discussion at beginning of sect.6 (zero eigenspace

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

Photometric and spectroscopic variations of the Be star HD 112999

Be objects are stars of B spectral type showing lines of the Balmer series in emission. The presence of these lines is attributed to the existence of an extended envelope, disk type, around them. Some stars are observed in both the Be and normal B-type spectroscopic states and they are known as transient Be stars. In this paper we show the analysis carried out on a new possible transient Be star, labelled HD 112999, using spectroscopic optical observations and photometric data.Comment: 10 pages, 5 figures, accepted for publication in IBV

The Spatial Orientation of Planetary Nebulae Within the Milky Way

We analyze the spatial orientation of a homogenous sample of 440 elongated Planetary Nebulae (PNe) in order to determine the orientation of their apparent major axis respect to the Milky Way plane. We present some important geometrical and statistical considerations that have been overlooked by the previous works on the subject. The global distribution of galactic position angles (GPA) of PNe is quantitatively not very different from a random distribution of orientations in the Galaxy. Nevertheless we find that there is at least one region on the sky, toward the galactic center, where a weak correlation may exist between the orientation of the major axis of some PNe and the Galactic equator, with an excess of axes with GPA$\sim 100^{\circ}$. Therefore, we confirm that ``extrinsic'' phenomena (i.e., global galactic magnetic fields, shell compression from motion relative to the Interstellar Medium) do not determine the morphology of PNe on most of the sky, with a possible exception towards the galactic center.Comment: 37 pages and 8 figures. Accepted for publication in PAS

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

On Information Theory, Spectral Geometry and Quantum Gravity

We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.Comment: 4 page

On the Time-Dependent Analysis of Gamow Decay

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wave functions. Observing that the time evolution of any wave function is given by its expansion in generalized eigenfunctions, we shall answer this question in the most straightforward manner, which at the same time is accessible to graduate students and specialists. Moreover the presentation can well be used in physics lectures to students.Comment: 10 pages, 4 figures; heuristic argument simplified, different example discussed, calculation of decay rate adde

Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the finiteness of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.Comment: 26 page