Fundamental solution method applied to time evolution of two energy level systems: exact and adiabatic limit results

A method of fundamental solutions has been used to investigate transitions in two energy level systems with no level crossing in a real time. Compact formulas for transition probabilities have been found in their exact form as well as in their adiabatic limit. No interference effects resulting from many level complex crossings as announced by Joye, Mileti and Pfister (Phys. Rev. {\bf A44} 4280 (1991)) have been detected in either case. It is argued that these results of this work are incorrect. However, some effects of Berry's phases are confirmed.Comment: LaTeX2e, 23 pages, 8 EPS figures. Style correcte

The high energy semiclassical asymptotics of loci of roots of fundamental solutions for polynomial potentials

In the case of polynomial potentials all solutions to 1-D Schroedinger equation are entire functions totally determined by loci of their roots and their behaviour at infinity. In this paper a description of the first of the two properties is given for fundamental solutions for the high complex energy limit when the energy is quantized or not. In particular due to the fact that the limit considered is semiclassical it is shown that loci of roots of fundamental solutions are collected of selected Stokes lines (called exceptional) specific for the solution considered and are distributed along these lines in a specific way. A stable asymptotic limit of loci of zeros of fundamental solutions on their exceptional Stokes lines has island forms and there are infintely many of such roots islands on exceptional Stokes lines escaping to infinity and a finite number of them on exceptional Stokes lines which connect pairs of turning points. The results obtained for asymptotic roots distributions of fundamental solutions in the semiclassical high (complex) energy limit are of a general nature for polynomial potentials.Comment: 41 pages, 14 figure

Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics

Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed for the corresponding Borel functions. Its main property is to order the singularity structure of the Borel plane in a hierarchical way by an increasing complexity of this structure starting from the analytic one. This allows us to study the Borel plane singularity structure in a systematic way. Examples of such structures are considered for linear, harmonic and anharmonic potentials. Together with the best approximation provided by the semiclassical series the exponentially small contribution completing the approximation are considered. A natural method of constructing such an exponential asymptotics relied on the Borel plane singularity structures provided by the topological expansion is developed. The method is used to form the semiclassical series including exponential contributions for the energy levels of the anharmonic oscillator.Comment: 46 pages, 22 EPS figure

Projective representation of k-Galilei group

The projective representations of k-Galilei group G_k are found by contracting the relevant representations of k-Poincare group. The projective multiplier is found. It is shown that it is not possible to replace the projective representations of G_k by vector representations of some its extension.Comment: 15 pages Latex fil

Crystallization of the ordered vortex phase in high temperature superconductors

The Landau-Khalatnikov time-dependent equation is applied to describe the crystallization process of the ordered vortex lattice in high temperature superconductors after a sudden application of a magnetic field. Dynamic coexistence of a stable ordered phase and an unstable disordered phase, with a sharp interface between them, is demonstrated. The transformation to the equilibrium ordered state proceeds by movement of this interface from the sample center toward its edge. The theoretical analysis dictates specific conditions for the creation of a propagating interface, and provides the time scale for this process.Comment: 8 pages and 3 figures; to be published in Phys. Rev. B (Rapid Communications section

Structural characterization of supramolecular assemblies by 13C spin dilution and 3D solid-state NMR.

13C spin diluted protein samples can be produced using [1-13C] and [2-13C]-glucose (Glc) carbon sources in the bacterial growth medium. The 13C spin dilution results in favorable 13C spectral resolution and polarization transfer behavior. We recently reported the combined use of [1-13C]- and [2-13C]-Glc labeling to facilitate the structural analysis of insoluble and non-crystalline biological systems by solid-state NMR (ssNMR), including sequential assignment, detection of long-range contacts and structure determination of macromolecular assemblies. In solution NMR the beneficial properties of sparsely labeled samples using [2-13C]-glycerol (13C labeled Cα sites on a 12C diluted background) have recently been exploited to provide a bi-directional assignment method (Takeuchi et al. in J Biomol NMR 49(1):17–26, 2011 ). Inspired by this approach and our own recent results using [2-13C]-Glc as carbon sources for the simplification of ssNMR spectra, we present a strategy for a bi-directional sequential assignment of solid-state NMR resonances and additionally the detection of long-range contacts using the combination of 13C spin dilution and 3D NMR spectroscopy. We illustrate our results with the sequential assignment and the collection of distance restraints on an insoluble and non-crystalline supramolecular assembly, the Salmonella typhimurium type III secretion system needle

Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems

A representation theory of the quantized Poincar\'e ($\kappa$-Poincar\'e) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the non-deformed Poincar\'e algebra. A theory of tensor operators for QPA is considered in detail. Necessary and sufficient conditions are found in order for scalars to be invariants. Covariant components of the four-momenta and the Pauli-Lubanski vector are explicitly constructed.These results are used for the construction of some q-relativistic equations. The Wigner-Eckart theorem for QPA is proven.Comment: 18 page

Utilisation de trois tests de génotoxicité pour l'étude de l'activité génotoxique de composés organohalogénés, d'acides fulviques chlorés et d'échantillons d'eau (non concentrés) en cours de traitement de potabilisation

Il est admis aujourd'hui que la génotoxicité identifiée dans les extraits d'eau potable provient principalement de l'action du chlore sur la matière organique naturelle qui donne naissance à des dérivés organohalogénés.Dans le présent travail, nous avons comparé la sensibilité de trois essais de génotoxicité (SOS chromotest, test d'Ames-fluctuation et test micronoyau triton) lors de l'étude de composés organohalogénés, d'acides fulviques chlorés et d'échantillons d'eau (non concentrés) en cours de traitement de potabilisation.Les composés organohalogénés étudiés sont 4 trihalométhanes, 5 acétonitriles et 5 chloropropanones identifiés dans l'eau potable ou dans des solutions de substances humiques chlorées. Les résultats obtenus révèlent que le SOS chromotest est globalement le moins sensible des trois essais et que le test d'Ames-fluctuation et le test micronoyau triton permettent généralement de détecter les plus faibles concentrations de composés génotoxiques. Les essais ont également permis de démontrer que la nature des substituants halogénés (brome ou chlore), le nombre et la position des atomes de chlore influencent notablement la génotoxicité des composés organohalogénés.Toutefois, les résultats obtenus indiquent qu'aucun des trois tests réalisés n'est suffisant à lui seul pour détecter l'ensemble des produits génotoxiques. Ces observations confirment la nécessité de réaliser une batterie de tests qui mette en oeuvre divers types cellulaires et différents systèmes de métabolisation, et détecte divers évènements de génotoxicité.Les travaux portant sur les solutions concentrées d'acides fulviques chlorés montrent l'intérêt des essais sur bactéries (particulièrement le test d'Ames-fluctuation) pour la détection rapide de l'activité génotoxique de ces solutions.L'étude concemant les échantillons d'eau prélevés à différents niveaux d'une station de potabilisation, et analysés sans concentration préalable, indique que le test d'Ames- fluctuation est le seul capable de détecter une activité génotoxique dans les échantillons non concentrés étudiés. On montre, conformément à la littérature, que l'activité mutagène observée résulte de la chloration de l'eau.Since the identification of organohalides in drinking water in 1974, several investigators have detected genotoxic activity in drinking water concentrates. It is now widely admitted that the observed genotoxicity originates mainly from the reaction of chlorine on natural organic matter contained in the raw water, which leads to the formation of organohalogenated compounds.The aim of this study is to show the benefit of three short-term assays for the evaluation of the genotoxic potency of organohalogenated compounds and of complex mixtures. In a wider context, the purpose is to identify a test or a battery of tests that can contribute to the control of natural and drinking water genotoxicity.The three genotoxicity assays carried out during this work were:- the SOS chromotest, a primary DNA damage in vitro assay on Escherichia coli; - the Ames- fluctuation test, a point mutation in vitro assay on Salmonella typhimurium; - and the newt micronucleus test, a chromosomal aberration in vivo assay on the amphibian Pleurodeles waltl. These assays display a valuable advantage: the water samples under study can be analyzed without concentration prior to testing. Thus, the different concentration procedures, which may modify the original genotoxicity of the water samples, are avoided.A previous study on seven reference genotoxic chemicals had indicated that the SOS chromotest was never the most sensitive of the three tests (for a given chemical, the most sensitive assay is defined as the test which detects the lowest concentration inducing a significant genotoxic effect). On the contrary, the Ames-fluctuation test proved to be the most sensitive for compounds showing direct genotoxic activity, and the newt micronucleus test the most sensitive for chemicals with indirect genotoxic effects. None of the assays was the most sensitive for every substance analyzed. These observations suggested the need to implement a battery of tests using several cell types, different metabolization systems and detecting several genotoxicity events. This earlier study also showed, in accord with several results in the literature, that the Ames-fluctuation test (in liquid medium) demonstrated a better sensitivity than the Ames test (in agar solid medium).The first part of the present study involved testing the genotoxicity of 14 organo- halogenated compounds identified in drinking water samples or in chlorinated humic matter samples. The chemicals studied were four chlorinated and/or brominated trihalomethanes (trichloro-, bromodichloro-, chlorodibromo- and tribromomethane), five chlorinated or brominated acetonitriles with one, two or three halogens (monochloro-, dichloro-, trichloro-, monobromo- and dibromoacetonitrile) and five chlorinated propanones with one, two or three substitutions on one or two carbon atoms (monochloro-, 1,1-dichloro-, 1,3-dichloro-, 1,1,1-trichloro- and 1,1,3- trichloropropanone). Although the SOS chromotest was the most sensitive for 3 of the 14 substances analyzed, the results confirmed that this test was globally the least sensitive; the Ames-fluctuation test and the newt micronucleus test remained the most efficient assays. It is interesting to note that the Ames-fluctuation test appeared the most sensitive for all the chloropropanones tested and the newt micronucleus test, for all the haloacetonitriles analyzed. Moreover, several structure-activity relationships were demonstrated: the nature of the halogenated substituents (bromine or chlorine), the number and, above all, the position of chlorine atoms strongly influenced the genotoxicity of the organohalides studied.In the second part of the work we analyzed the effects of complex mixtures containing several organohalogenated compounds: the three tests were performed on two chlorinated fulvic acids of different origin. Pornic fulvic acid was extracted from a surface water reservoir used to produce drinking water in Vendée (France) and Pinail fulvic acid came from a forest pond near Poitiers (France). The total organic carbon was about 1 g/l in the solution subjected to chlorination and the molar chlorination ratio was 1.5 Cl2/C. The results showed the advantage of tests using bacteria: the Ames fluctuation test was the only assay able to detect the genotoxicity of both chlorinated fulvic acids; the SOS chromotest detected the genotoxic effect of only one of the chlorinated fulvic acids (Pinail). In contrast, the newt micronucleus test did not show any genotoxicity of the chlorinated fulvic acids. However, it must be pointed out that, as insufficient fulvic acid was available, the genotoxic potency of these solutions on the newt was not tested under adequate conditions (e.g., subchronic concentrations were not studied). Nevertheless, the concentrations of fulvic acid analyzed were very close to those found in the aquatic environment.The last part of the study attempted to approximate environmental and human exposure conditions: the three tests were performed on four water samples taken at several stages of a drinking water treatment plant. These samples were analyzed for genotoxicity in the three test systems without preconcentration. The plant studied is characterized by the following treatment steps: - coagulation-flocculation; - chlorination at 6 g Cl2/m3; - sand filtration; - ozonation at 1.9 g O3/m3; - final chlorination at 1.4 g Cl2/m3 before sending the treated water into the distribution system. The four samples were taken:1. before any treatment (raw water, 10 to 13 mg total organic carbon per liter), 2. between the sand layer filter and the ozonator (chlorinated water), 3. after the ozonator (ozonated water), 4. and at the end of the treatment process (treated water). The results obtained confirmed the advantage of the Ames fluctuation test, which was the only assay able to detect a genotoxic activity in the unconcentrated water samples studied. Regarding the influence of the different chemical treatments on the mutagenicity observed, it was demonstrated that the first chlorination step led to the formation of direct-acting mutagens. The treatment with ozone, at the rate used, did not significantly modify the mutagenicity of the samples that had previously been chlorinated. Similarly, the second chlorination step did not significantly increase the direct mutagenicity detected.Practically, our study indicated that the Ames-fluctuation test is the only assay, among the three performed that is able to contribute efficiently to the control of drinking water genotoxicity. In this context, the benefit of the SOS chromotest appears only in case of accidental pollution: indeed, it is the only test able to yield results within 24 hours. The implementation of the newt micronucleus test could be useful for the control of natural or drinking water genotoxicity in case of extensive pollution