gln+1 ALGEBRA OF MATRIX DIFFERENTIAL OPERATORS AND MATRIX QUASI-EXACTLY-SOLVABLE PROBLEMS

The generators of the algebra gln+1 in the form of differential operators of the first order acting on Rn with matrix coefficients are explicitly written. The algebraic Hamiltonians for matrix generalization of 3−body Calogero and Sutherland models are presented

The dual Hahn q-polynomials in the lattice x(s) = [s]q[s + 1] q and the q-Algebras SUq(2) and SUq(1; 1)

The dual q-Hahn polynomials in the non uniform lattice x(s) = [s]q[s + 1]q are obtained. The main data for these polynomials are calculated ( the square of the norm the coe cients of the three term recurrence relation, etc), as well as its representation as a q-hypergeometric series. The connection with the Clebsch-Gordan Coe cients of the Quantum Algebras SUq (2) and SUq (1; 1) is also given.Comisión Interministerial de Ciencia y TecnologíaInstituto de Física (Universidad Nacional Autónoma de México)Consejo Nacional de Ciencia, Tecnología e Innovación (México

q-Deformed Vibron model for diatomic molecules

A deformed version of the vibron model for diatomic molecules is constructed. Both the O(4) and U(3) dynamical symmetries of the model are rewritten, using the concept of complementary subalgebras, in a more convenient form, which is subsequently deformed. The present model unifies the so far independent successful quantum-algebraic approaches to rotational and to vibrational spectra of diatomic molecules. In addition, the method can be used for the construction of deformed versions of the U(5) and O(6) limits of the interacting boson model of nuclear structure

A q-analog of the Racah polynomials and the q-algebra SUq(2)

We study some q-analogues of the Racah polynomials and some of their applications in the theory of representation of quantum algebras.Dirección General de Enseñanza SuperiorPlan Andaluz de Investigación (Junta de Andalucía)Russian Foundation of Basic researc

Closed geodesics and billiards on quadrics related to elliptic KdV solutions

We consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards. Namely, generic complex invariant manifolds are not Abelian varieties, and the billiard map is no more algebraic. A Poncelet-like theorem for such system is known. We give explicit sufficient conditions both for closed geodesics and periodic billiard orbits on Q and discuss their relation with the elliptic KdV solutions and elliptic Calogero systemComment: 23 pages, Latex, 1 figure Postscrip

SU(3) realization of the rigid asymmetric rotor within the IBM

It is shown that the spectrum of the asymmetric rotor can be realized quantum mechanically in terms of a system of interacting bosons. This is achieved in the SU(3) limit of the interacting boson model by considering higher-order interactions between the bosons. The spectrum corresponds to that of a rigid asymmetric rotor in the limit of infinite boson number.Comment: 9 pages, 2 figures, LaTeX, epsfi

Fano resonances in nanoscale structures

Nowadays nanotechnology allows to scale-down various important devices (sensors, chips, fibres, etc), and, thus, opens up new horizon for their applications. Nevertheless, the efficiency most of them is still based on the fundamental physical phenomena, such as resonances. Thus, the understanding of the resonance phenomena will be beneficial. One of the well-known examples is the resonant enhancement of the transmission known as Breit-Wigner resonances, which can be described by a Lorentzian function. But, in many physical systems the scattering of waves involves propagation along different paths, and, as a consequence, results in interference phenomena, where constructive interference corresponds to resonant enhancement and destructive interference to resonant suppression of the transmission. Recently, a variety of experimental and theoretical work has revealed such patterns in different branches of physics. The purpose of this Review is to demonstrate that this kind of resonant scattering is related to the Fano resonances, known from atomic physics. One of the main features of the Fano resonances is the asymmetric profile. The asymmetry comes from the close coexistence of resonant transmission and resonant reflection. Fano successfully explained such a phenomenon in his seminal paper in 1961 in terms of interaction of a discrete (localized) state with a continuum of propagation modes. It allows to describe both resonant enhancement and resonant suppression in a unified manner. All of these properties can be demonstrated in the frame of a very simple model, which will be used throughout the Review to show that resonant reflections observed in different complex systems are indeed closely related to the Fano resonances.Comment: This review paper was submitted to Review of Modern Physics. But all comments are still welcome

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure

Azimuthal anisotropy at RHIC: the first and fourth harmonics

We report the first observations of the first harmonic (directed flow, v_1), and the fourth harmonic (v_4), in the azimuthal distribution of particles with respect to the reaction plane in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). Both measurements were done taking advantage of the large elliptic flow (v_2) generated at RHIC. From the correlation of v_2 with v_1 it is determined that v_2 is positive, or {\it in-plane}. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 6 pages with 3 figures, as accepted for Phys. Rev. Letters The data tables are at http://www.star.bnl.gov/central/publications/pubDetail.php?id=3

Strong reduction of the off-momentum halo in crystal assisted collimation of the SPS beam

A study of crystal assisted collimation has been continued at the CERN SPS for different energies of stored beams using 120 GeV/. c and 270 GeV/. c protons and Pb ions with 270 GeV/. c per charge. A bent silicon crystal used as a primary collimator deflected halo particles using channeling and directing them into the tungsten absorber. A strong correlation of the beam losses in the crystal and off-momentum halo intensity measured in the first high dispersion (HD) area downstream was observed. In channeling conditions, the beam loss rate induced by inelastic interactions of particles with nuclei is significantly reduced in comparison with the non-oriented crystal. A maximal reduction of beam losses in the crystal larger than 20 was observed with 270 GeV/. c protons. The off-momentum halo intensity measured in the HD area was also strongly reduced in channeling conditions. The reduction coefficient was larger than 7 for the case of Pb ions. A strong loss reduction was also detected in regions of the SPS ring far from the collimation area. It was shown by simulations that the miscut angle between the crystal surface and its crystallographic planes doubled the beam losses in the aligned crystal.peer-reviewe