57,463 research outputs found

    Effective Operator Treatment of the Lipkin Model

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    We analyze the Lipkin Model using effective operator techniques. We present both analytical and numerical results for effective Hamiltonians. The accuracy of the cluster approximation is investigated.Comment: To appear in Phys.Rev.

    Structure of the constituent quark and quark distributions of hadrons

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    We study the structure of constituent quarks by dressing bare quarks with the Goldstone bosons and its implications for quark distribution functions of hadrons f1(x)f_1(x), g1(x)g_1(x) and h1(x)h_1(x). In particular we discuss effects of the dressing on the nucleon spin structure, and find that contributions to chiral-odd h1(x)h_1(x) is quite different from those to g1(x)g_1 (x), which can be measured in the semi-inclusive polarized deep inelastic scattering.Comment: 7 pages, LaTeX, 4 figures are included using epsfig.sty, talk presented at QULEN97, to appear in the proceedings, Complete PS fils is also available at http://WWW.physik.tu-muenchen.de/~ksuzuki/publication.htm

    Multiresolution approximation of the vector fields on T^3

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    Multiresolution approximation (MRA) of the vector fields on T^3 is studied. We introduced in the Fourier space a triad of vector fields called helical vectors which derived from the spherical coordinate system basis. Utilizing the helical vectors, we proved the orthogonal decomposition of L^2(T^3) which is a synthesis of the Hodge decomposition of the differential 1- or 2-form on T^3 and the Beltrami decomposition that decompose the space of solenoidal vector fields into the eigenspaces of curl operator. In the course of proof, a general construction procedure of the divergence-free orthonormal complete basis from the basis of scalar function space is presented. Applying this procedure to MRA of L^2(T^3), we discussed the MRA of vector fields on T^3 and the analyticity and regularity of vector wavelets. It is conjectured that the solenoidal wavelet basis must break r-regular condition, i.e. some wavelet functions cannot be rapidly decreasing function because of the inevitable singularities of helical vectors. The localization property and spatial structure of solenoidal wavelets derived from the Littlewood-Paley type MRA (Meyer's wavelet) are also investigated numerically.Comment: LaTeX, 33 Pages, 3 figures. submitted to J. Math. Phy
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