Invariant vector fields and the prolongation method for supersymmetric quantum systems

The kinematical and dynamical symmetries of equations describing the time evolution of quantum systems like the supersymmetric harmonic oscillator in one space dimension and the interaction of a non-relativistic spin one-half particle in a constant magnetic field are reviewed from the point of view of the vector field prolongation method. Generators of supersymmetries are then introduced so that we get Lie superalgebras of symmetries and supersymmetries. This approach does not require the introduction of Grassmann valued differential equations but a specific matrix realization and the concept of dynamical symmetry. The Jaynes-Cummings model and supersymmetric generalizations are then studied. We show how it is closely related to the preceding models. Lie algebras of symmetries and supersymmetries are also obtained.Comment: 37 pages, 7 table

AMBER on the VLTI: data processing and calibration issues

We present here the current performances of the AMBER / VLTI instrument for standard use and compare these with the offered modes of the instrument. We show that the instrument is able to reach its specified precision only for medium and high spectral resolution modes, differential observables and bright objects. For absolute observables, the current achievable accuracy is strongly limited by the vibrations of the Unit Telescopes, and also by the observing procedure which does not take into account the night-long transfer function monitoring. For low-resolution mode, the current limitation is more in the data reduction side, since several effects negligible at medium spectral resolution are not taken into account in the current pipeline. Finally, for faint objects (SNR around 1 per spectral channel), electromagnetic interferences in the VLTI interferometric laboratory with the detector electronics prevents currently to get unbiased measurements. Ideas are under study to correct in the data processing side this effect, but a hardware fix should be investigated seriously since it limits seriously the effective limiting magnitude of the instrument.Comment: 10 page

Cellulose nanocarriers via miniemulsion allow Pathogen-Specific agrochemical delivery

The current spraying of agrochemicals is unselective and ineffective, consuming a high amount of fungicides, which endangers the environment and human health. Cellulose-based nanocarriers (NCs) are a promising tool in sustainable agriculture and suitable vehicles for stimuli-responsive release of agrochemicals to target cellulase-segregating fungi, which cause severe plant diseases such as Apple Canker. Herein, cellulose was modified with undec-10-enoic acid to a hydrophobic and cross-linkable derivative, from which NCs were prepared via thiol-ene addition in miniemulsion. During the crosslinking reaction, the NCs were loaded in situ with hydrophobic fungicides, Captan and Pyraclostrobin. NCs with average sizes ranging from 200 to 300 nm and an agrochemical-load of 20 wt% were obtained. Cellulose-degrading fungi, e.g. Neonectria. ditissima which is responsible for Apple Canker, lead to the release of fungicides from the aqueous NC dispersions suppressing fungal growth. In contrast, the non-cellulase segregating fungi, e.g. Cylindrocladium buxicola, do not degrade the agrochemical-loaded NCs. This selective action against Apple Canker fungi, N. ditissima, proves the efficacy of NC-mediated drug delivery triggered by degradation in the exclusive presence of cellulolytic fungi. Cellulose NCs represent a sustainable alternative to the current unselective spraying of agrochemicals that treats many crop diseases ineffectively

Fuzzy Torus via q-Parafermion

We note that the recently introduced fuzzy torus can be regarded as a q-deformed parafermion. Based on this picture, classification of the Hermitian representations of the fuzzy torus is carried out. The result involves Fock-type representations and new finite dimensional representations for q being a root of unity as well as already known finite dimensional ones.Comment: 12pages, no figur

Axially Symmetric Bianchi I Yang-Mills Cosmology as a Dynamical System

We construct the most general form of axially symmetric SU(2)-Yang-Mills fields in Bianchi cosmologies. The dynamical evolution of axially symmetric YM fields in Bianchi I model is compared with the dynamical evolution of the electromagnetic field in Bianchi I and the fully isotropic YM field in Friedmann-Robertson-Walker cosmologies. The stochastic properties of axially symmetric Bianchi I-Einstein-Yang-Mills systems are compared with those of axially symmetric YM fields in flat space. After numerical computation of Liapunov exponents in synchronous (cosmological) time, it is shown that the Bianchi I-EYM system has milder stochastic properties than the corresponding flat YM system. The Liapunov exponent is non-vanishing in conformal time.Comment: 18 pages, 6 Postscript figures, uses amsmath,amssymb,epsfig,verbatim, to appear in CQ

First year of results from a mooring over a Posidonia Oceanica seagrass meadow (Corsica, France)

peer reviewe

On realizations of nonlinear Lie algebras by differential operators

We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear, quadratic and cubic cases are explicitly visited but the method works for arbitrary degrees in the polynomial functions. Multi-boson Hamiltonians are studied in the context of these ``nonlinear'' Lie algebras and some examples dealing with quantum optics are pointed out.Comment: 21 pages, Latex; New examples added in Sect.

Polynomial algebras and exact solutions of general quantum non-linear optical models I: Two-mode boson systems

We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe ansatz) solutions to a class of 2-mode boson systems, including the Boson-Einstein Condensate models as special cases. Up to an overall factor, the eigenfunctions of the 2-mode boson systems are given by polynomials whose roots are solutions of the associated Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of these roots. We also establish the spectral equivalence between the BEC models and certain quasi-exactly solvable Sch\"ordinger potentials.Comment: 20 pages, final version to appear in J. Phys. A: Math. Theor

Lowest weight representations of super Schrodinger algebras in low dimensional spacetime

We investigate the lowest weight representations of the super Schrodinger algebras introduced by Duval and Horvathy. This is done by the same procedure as the semisimple Lie algebras. Namely, all singular vectors within the Verma modules are constructed explicitly then irreducibility of the associated quotient modules is studied again by the use of singular vectors. We present the classification of irreducible Verma modules for the super Schrodinger algebras in (1+1) and (2+1) dimensional spacetime with N = 1, 2 extensions.Comment: 10pages, talk given at GROUP28 conference New Castle 26-30th July 2010, reference adde