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

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

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

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

A Subpopulation of Adult Skeletal Muscle Stem Cells Retains All Template DNA Strands after Cell Division

SummarySatellite cells are adult skeletal muscle stem cells that are quiescent and constitute a poorly defined heterogeneous population. Using transgenic Tg:Pax7-nGFP mice, we show that Pax7-nGFPHi cells are less primed for commitment and have a lower metabolic status and delayed first mitosis compared to Pax7-nGFPLo cells. Pax7-nGFPHi can give rise to Pax7-nGFPLo cells after serial transplantations. Proliferating Pax7-nGFPHi cells exhibit lower metabolic activity, and the majority performs asymmetric DNA segregation during cell division, wherein daughter cells retaining template DNA strands express stem cell markers. Using chromosome orientation-fluorescence in situ hybridization, we demonstrate that all chromatids segregate asymmetrically, whereas Pax7-nGFPLo cells perform random DNA segregation. Therefore, quiescent Pax7-nGFPHi cells represent a reversible dormant stem cell state, and during muscle regeneration, Pax7-nGFPHi cells generate distinct daughter cell fates by asymmetrically segregating template DNA strands to the stem cell. These findings provide major insights into the biology of stem cells that segregate DNA asymmetrically

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

A Subpopulation of Adult Skeletal Muscle Stem Cells Retains All Template DNA Strands after Cell Division

SummarySatellite cells are adult skeletal muscle stem cells that are quiescent and constitute a poorly defined heterogeneous population. Using transgenic Tg:Pax7-nGFP mice, we show that Pax7-nGFPHi cells are less primed for commitment and have a lower metabolic status and delayed first mitosis compared to Pax7-nGFPLo cells. Pax7-nGFPHi can give rise to Pax7-nGFPLo cells after serial transplantations. Proliferating Pax7-nGFPHi cells exhibit lower metabolic activity, and the majority performs asymmetric DNA segregation during cell division, wherein daughter cells retaining template DNA strands express stem cell markers. Using chromosome orientation-fluorescence in situ hybridization, we demonstrate that all chromatids segregate asymmetrically, whereas Pax7-nGFPLo cells perform random DNA segregation. Therefore, quiescent Pax7-nGFPHi cells represent a reversible dormant stem cell state, and during muscle regeneration, Pax7-nGFPHi cells generate distinct daughter cell fates by asymmetrically segregating template DNA strands to the stem cell. These findings provide major insights into the biology of stem cells that segregate DNA asymmetrically

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.Comment: version accepted for publication in J. Math. Phys.: criterion excluding basis property (Proposition 6) added, unbounded time-evolution discussed, new reference

Krein Spaces in de Sitter Quantum Theories

Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group SO0(1,4) or Sp(2,2) as an appealing substitute to the flat space-time Poincaré relativity. Quantum elementary systems are then associated to unitary irreducible representations of that simple Lie group. At the lowest limit of the discrete series lies a remarkable family of scalar representations involving Krein structures and related undecomposable representation cohomology which deserves to be thoroughly studied in view of quantization of the corresponding carrier fields. The purpose of this note is to present the mathematical material needed to examine the problem and to indicate possible extensions of an exemplary case, namely the so-called de Sitterian massless minimally coupled field, i.e. a scalar field in de Sitter space-time which does not couple to the Ricci curvature