Semi-classical behavior of P\"oschl-Teller coherent states

We present a construction of semi-classical states for P\"oschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They minimize a special uncertainty relation. Like standard coherent states they resolve the identity with a uniform measure. They permit to establish the correspondence (quantization) between classical and quantum quantities. Finally, their time evolution is localized on the classical phase space trajectory.Comment: 7 pages, 2 figures, 1 animatio

Serodiagnosis of infectious mononucleosis by using recombinant Epstein-Barr virus antigens and enzyme-linked immunosorbent assay technology

Four recombinant, diagnostically useful Epstein-Barr virus (EBV) proteins representative of the viral capsid antigen (p150), diffuse early antigen (p54), the major DNA-binding protein (p138), and the EBV nuclear antigen (p72) (W. Hinderer, H. Nebel-Schickel, H.H. Sonneborn, M. Motz, R. Kühbeck, and H. Wolf, J. Exp. Clin. Cancer Res. 7[Suppl.]:132, 1988) were used to set up individual enzyme-linked immunosorbent assays (ELISAs) for the qualitative and quantitative detection of immunoglobulin M (IgM) and IgG antibodies. In direct comparison with results obtained by standard immunofluorescence or immunoperoxidase assays, it was then shown that the recombinant EBV ELISAs provide the means for specific and sensitive serodiagnosis of infectious mononucleosis (IM) caused by EBV. The most useful markers in sera from such patients proved to be IgM antibodies against p54, p138, and p150. Additional positive markers for recent or ongoing IM apparently were IgG antibodies against p54 and p138. In contrast, anti-p72 IgG had a high preference for sera from healthy blood donors and, therefore, can be considered indicative of past exposure to the virus. Altogether, the individual ELISAs proved to be as specific and at least as sensitive for the diagnosis of IM as the currently available standard techniques are. Moreover, our findings suggest that, by combining individual test antigens, a workable ELISA system consisting of three assays (IgM against p54, p138, and p150; IgG against p54 and p138; and IgG against p72) can be established for the standardized rapid diagnosis of acute EBV infections

New SUSYQM coherent states for Poschl-Teller potentials: a detailed mathematical analysis

In a recent short note [Bergeron H, Gazeau J P, Siegl P and Youssef A 2010 EPL 92 60003], we have presented the nice properties of a new family of semi-classical states for P\"oschl-Teller potentials. These states are built from a supersymmetric quantum mechanics approach and the parameters of these "coherent" states are points in the classical phase space. In this article we develop all the mathematical aspects that have been left apart in the previous article (proof of the resolution of unity, detailed calculations of quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self- adjointness or self-adjoint extensions). Some additional questions as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of P\"oschl-Teller potentials

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

The Pauli equation with complex boundary conditions

We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.Comment: 16 pages, 4 figure

Palynomorphs of the Normapolles group and related plant mesofossils from the Iharkút vertebrate site, Bakony Mountains (Hungary)

Abstract Palynological and paleobotanical investigation of bonebeds and other strata of the Csehbánya Formation from the vertebrate locality at Iharkút (Bakony Mts, Hungary) reveals well-preserved Santonian palynological assemblages dominated by the Normapolles group, with a minor component consisting of other angiosperm pollen, some gymnosperm pollen, and spores. Eleven species of Normapolles-type pollen grains belonging to seven genera and fruit remains of a new taxon, Sphaeracostata barbackae gen. et sp. nov., are described. The new species is very abundant in the material, represented by ca. 1000 specimens. The genus Caryanthus Friis and an unnamed form previously reported from Haţeg by Lindfors et al. (2010) are also present. Plants producing Normapolles-type pollen grains diversified during the Late Cretaceous, with a bloom in the Santonian. The palynostratigraphy of the Upper Cretaceous terrestrial sediments in the studied region is based on Normapolles-related species. The studied assemblage is assigned to the Oculopollis zaklinskaiae-Tetracolporopollenites (Brecolpites) globosus Zone (or Zone C) indicating a late Santonian age. Comparison of the Iharkút palynoflora with other known Upper Cretaceous palynofloras of Central Europe shows diachronous occurrence of Normapolles taxa at different geographic localities and warrants further investigation. The ecological requirements of the amphibian fauna reflect azonal conditions controlled by the availability of water, which is in agreement with the inferred ecological conditions based on the paleobotanical investigations. The fauna is of entirely non-marine character, further supported by isotope studies, in line with our data showing that the palynological samples contain no marine forms

PT-symmetric models in curved manifolds

We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.Comment: 37 pages, PDFLaTeX with 11 figure