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

Diagnostics-in-a-Suitcase: Development of a portable and rapid assay for the detection of the emerging avian influenza A (H7N9) virus

Background: In developing countries, the necessary equipment for the diagnosis is only available in few central laboratories, which are less accessible and of limited capacity to test large numbers of incoming samples. Moreover, transport conditions of samples are inadequate and therefore lead to unreliable results. Objectives: The development of rapid, inexpensive, and simple test would allow mobile detection of viruses. Study Design: A suitcase laboratory “Diagnostics-in-a-Suitcase” (56 × 45.5 × 26.5 cm) containing all necessary reagents and devices to perform reverse transcription recombinase polymerase amplification (RT-RPA) assay was developed. As an example, Two RT-RPA assays for the detection of hemagglutinin (H) and neuraminidase (N) genes of the novel avian influenza (H7N9) virus were established. Results: Sensitivities were 10 and 100 \{RNA\} molecules for the \{H7\} and the \{N9\} RT-RPA assays, respectively. Assays were performed at a single temperature (42 °C). Results were obtained within 2-7 minutes. The \{H7N9\} RT-RPA assays showed neither a cross-detection of any other respiratory viruses affecting humans and/or birds nor of the human or chicken genomes. All reagents were used, stored, and transported at ambient temperature, i.e. cold chain independent. In addition, the Diagnostics-in-a-Suitcase was operated by a solar power battery. Conclusions: The developed assay protocol and mobile setup performed well. Moreover, it can be easily implemented to perform diagnosis at airport, quarantine stations, or farms for rapid on-site viral nucleic acid detection

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

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

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

Perturbation Theory of Schr\"odinger Operators in Infinitely Many Coupling Parameters

In this paper we study the behavior of Hamilton operators and their spectra which depend on infinitely many coupling parameters or, more generally, parameters taking values in some Banach space. One of the physical models which motivate this framework is a quantum particle moving in a more or less disordered medium. One may however also envisage other scenarios where operators are allowed to depend on interaction terms in a manner we are going to discuss below. The central idea is to vary the occurring infinitely many perturbing potentials independently. As a side aspect this then leads naturally to the analysis of a couple of interesting questions of a more or less purely mathematical flavor which belong to the field of infinite dimensional holomorphy or holomorphy in Banach spaces. In this general setting we study in particular the stability of selfadjointness of the operators under discussion and the analyticity of eigenvalues under the condition that the perturbing potentials belong to certain classes.Comment: 25 pages, Late

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

Reverse transcription recombinase polymerase amplification assay for the detection of middle East respiratory syndrome coronavirus

The emergence of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in the eastern Mediterranean and imported cases to Europe has alerted public health authorities. Currently, detection of MERS-CoV in patient samples is done by real-time RT-PCR. Samples collected from suspected cases are sent to highly-equipped centralized laboratories for screening. A rapid point-of-care test is needed to allow more widespread mobile detection of the virus directly from patient material. In this study, we describe the development of a reverse transcription isothermal Recombinase Polymerase Amplification (RT-RPA) assay for the identification of MERS-CoV. A partial nucleocapsid gene RNA molecular standard of MERS-coronavirus was used to determine the assay sensitivity. The isothermal (42°C) MERS-CoV RT-RPA was as sensitive as real-time RT-PCR (10 RNA molecules), rapid (3-7 minutes) and mobile (using tubescanner weighing 1kg). The MERS-CoV RT-RPA showed cross-detection neither of any of the RNAs of several coronaviruses and respiratory viruses affecting humans nor of the human genome. The developed isothermal real-time RT-RPA is ideal for rapid mobile molecular MERS-CoV monitoring in acute patients and may also facilitate the search for the animal reservoir of MERS-CoV

Inequivalent quantizations of the three-particle Calogero model constructed by separation of variables

We quantize the 1-dimensional 3-body problem with harmonic and inverse square pair potential by separating the Schr\"odinger equation following the classic work of Calogero, but allowing all possible self-adjoint boundary conditions for the angular and radial Hamiltonians. The inverse square coupling constant is taken to be $g=2\nu (\nu-1)$ with ${1/2} <\nu< {3/2}$ and then the angular Hamiltonian is shown to admit a 2-parameter family of inequivalent quantizations compatible with the dihedral $D_6$ symmetry of its potential term $9 \nu (\nu -1)/\sin^2 3\phi$. These are parametrized by a matrix $U\in U(2)$ satisfying $\sigma_1 U \sigma_1 = U$, and in all cases we describe the qualitative features of the angular eigenvalues and classify the eigenstates under the $D_6$ symmetry and its $S_3$ subgroup generated by the particle exchanges. The angular eigenvalue $\lambda$ enters the radial Hamiltonian through the potential $(\lambda -{1/4})/r^2$ allowing a 1-parameter family of self-adjoint boundary conditions at $r=0$ if $\lambda <1$. For $0<\lambda<1$ our analysis of the radial Schr\"odinger equation is consistent with previous results on the possible energy spectra, while for $\lambda <0$ it shows that the energy is not bounded from below rejecting those $U$'s admitting such eigenvalues as physically impermissible. The permissible self-adjoint angular Hamiltonians include, for example, the cases $U=\pm {\bf 1}_2, \pm \sigma_1$, which are explicitly solvable and are presented in detail. The choice $U=-{\bf 1}_2$ reproduces Calogero's quantization, while for the choice $U=\sigma_1$ the system is smoothly connected to the harmonic oscillator in the limit $\nu \to 1$.Comment: 45 pages, 6 figures, LaTeX, v2: a reference and a note added, v3: merely a constant is correcte

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