Norm kernels and the closeness relation for Pauli-allowed basis functions

The norm kernel of the generator-coordinate method is shown to be a symmetric kernel of an integral equation with eigenfunctions defined in the Fock--Bargmann space and forming a complete set of orthonormalized states (classified with the use of SU(3) symmetry indices) satisfying the Pauli exclusion principle. This interpretation allows to develop a method which, even in the presence of the SU(3) degeneracy, provides for a consistent way to introduce additional quantum numbers for the classification of the basis states. In order to set the asymptotic boundary conditions for the expansion coefficients of a wave function in the SU(3) basis, a complementary basis of functions with partial angular momenta as good quantum numbers is needed. Norm kernels of the binary systems 6He+p, 6He+n, 6He+4He, and 8He+4He are considered in detail.Comment: 25 pages; submitted to Few-Body System

Formation of a rotating jet during the filament eruption on 10-11 April 2013

We analyze multi-wavelength and multi-viewpoint observations of a helically twisted plasma jet formed during a confined filament eruption on 10-11 April 2013. Given a rather large scale event with its high spatial and temporal resolution observations, it allows us to clearly understand some new physical details about the formation and triggering mechanism of twisting jet. We identify a pre-existing flux rope associated with a sinistral filament, which was observed several days before the event. The confined eruption of the filament within a null point topology, also known as an Eiffel tower (or inverted-Y) magnetic field configuration results in the formation of a twisted jet after the magnetic reconnection near a null point. The sign of helicity in the jet is found to be the same as that of the sign of helicity in the filament. Untwisting motion of the reconnected magnetic field lines gives rise to the accelerating plasma along the jet axis. The event clearly shows the twist injection from the pre-eruptive magnetic field to the jet.Comment: 14 pages, 12 figures, to appear in MNRA

Peculiar properties of the cluster-cluster interaction induced by the Pauli exclusion principle

Role of the Pauli principle in the formation of both the discrete spectrum and multi-channel states of the binary nuclear systems composed of clusters is studied in the Algebraic Version of the resonating-group method. Solutions of the Hill-Wheeler equations in the discrete representation of a complete basis of the Pauli-allowed states are discussed for 4He+n, 3H+3H, and 4He+4He binary systems. An exact treatment of the antisymmetrization effects are shown to result in either an effective repulsion of the clusters, or their effective attraction. It also yields a change in the intensity of the centrifugal potential. Both factors significantly affect the scattering phase behavior. Special attention is paid to the multi-channel cluster structure 6He+6He as well as to the difficulties arising in the case when the two clustering configurations, 6He+6He and 4He+8He, are taken into account simultaneously. In the latter case the Pauli principle, even in the absence of a potential energy of the cluster-cluster interaction, leads to the inelastic processes and secures an existence of both the bound state and resonance in the 12Be compound nucleus.Comment: 17 pages, 14 figures, 1 table; submitted to Phys.Rev.C Keywords: light neutron-rich nuclei, cluster model

Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics

Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation of quantum mechanics. A SIC-POVM is shown to be a special case of the probability representation. The problem of SIC-POVM existence is formulated in terms of symbols of operators associated with a star-product quantization scheme. We show that SIC-POVMs (if they do exist) must obey general rules of the star product, and, starting from this fact, we derive new relations on SIC-projectors. The case of qubits is considered in detail, in particular, the relation between the SIC probability representation and other probability representations is established, the connection with mutually unbiased bases is discussed, and comments to the Lie algebraic structure of SIC-POVMs are presented.Comment: 22 pages, 1 figure, LaTeX, partially presented at the Workshop "Nonlinearity and Coherence in Classical and Quantum Systems" held at the University "Federico II" in Naples, Italy on December 4, 2009 in honor of Prof. Margarita A. Man'ko in connection with her 70th birthday, minor misprints are corrected in the second versio

Hydrofoil flow over the interface of a two-layer heavy fluid with a free surface and rigid bottom

The theory of small-amplitude waves is used to analyze the hydrofoil flow of a two-layer heavy fluid. The upper layer is bounded by a free surface, while the lower layer is bounded by a horizontal bottom. simulation of boundaries by singularities. Due to this method, the boundary condition specified on the contour is satisfied analytically exactly. By using the interface conditions, the problem is reduced to two systems of three singular integrodifferential equations. A special regularization technique gives systems of linear integral equations, which are solved numerically by applying the method of successive approximations with the use of a specially developed algorithm and a FORTRAN program. The numerical-analytical method developed applies to a wing section of arbitrary, including actual, shape placed in a fluid flow with interfaces of various types. The computations were performed for a NACA 66mod hydrofoil. The influence exerted by the angle of attack and the interfaces on the hydrodynamic hydrofoil characteristics is investigated in different ranges of Froude numbers. Shapes of internal and surface waves are obtained. Hydrodynamic effects associated with the dead water phenomenon are detected. © 2010 Pleiades Publishing, Ltd

On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation. We use these results to show that every orthosupersymmetric system of order $p$ has a parasupersymmetry of order $p$ and a fractional supersymmetry of order $p+1$.Comment: 13 pages, to appear in J. Phys. A: Math. Ge