4,997 research outputs found

    Dynamical correlation functions in the Calogero-Sutherland model

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    We compute the dynamical Green function and density-density correlation in the Calogero-Sutherland model for all integer values of the coupling constant. An interpretation of the intermediate states in terms of quasi-particles is found.Comment: 20pgs, (1 reference added

    Excited States of Calogero-Sutherland Model and Singular Vectors of the WNW_N Algebra

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    Using the collective field method, we find a relation between the Jack symmetric polynomials, which describe the excited states of the Calogero-Sutherland model, and the singular vectors of the WNW_N algebra. Based on this relation, we obtain their integral representations. We also give a direct algebraic method which leads to the same result, and integral representations of the skew-Jack polynomials.Comment: LaTeX, 29 pages, 2 figures, New sections for skew-Jack polynomial and example of singular vectors adde

    Student Learning Outcomes of an Interdisciplinary Fashion Event

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    The purposes of a cross-college fashion show held at a Mid-Atlantic university were to: a) provide a platform for developing or emergent professionals to display their career talents, b) provide an opportunity for students to work collaboratively across multiple creative disciplines, c) give students a holistic academic experience, and d) support undergraduate scholarships. Such an interdisciplinary event for students from various majors across a university may stimulate the growth of knowledge and motivate real-life applications

    Anyon Basis of c=1 Conformal Field Theory

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    We study the c=1c=1 conformal field theory of a free compactified boson with radius r=βr=\sqrt{\beta} (β\beta is an integer). The Fock space of this boson is constructed in terms of anyon vertex operators and each state is labeled by an infinite set of pseudo-momenta of filled particles in pseudo-Dirac sea. Wave function of multi anyon state is described by an eigenfunction of the Calogero-Sutherland (CS) model. The c=1c=1 conformal field theory at r=βr=\sqrt{\beta} gives a field theory of CS model. This is a natural generalization of the boson-fermion correspondence in one dimension to boson-anyon correspondence. There is also an interesting duality between anyon with statistics θ=π/β\theta=\pi/\beta and particle with statistics θ=βπ\theta=\beta \pi.Comment: 17 page

    Single particle Green's function in the Calogero-Sutherland model for rational couplings β=p/q\beta=p/q

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    We derive an exact expression for the single particle Green function in the Calogero-Sutherland model for all rational values of the coupling β\beta. The calculation is based on Jack polynomial techniques and the results are given in the thermodynamical limit. Two type of intermediate states contribute. The firts one consists of a particle propagating out of the Fermi sea and the second one consists of a particle propagating in one direction, q particles in the opposite direction and p holes.Comment: 9 pages, RevTeX, epsf.tex, 4 figures, files uuencode

    Correspondence between conformal field theory and Calogero-Sutherland model

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    We use the Jack symmetric functions as a basis of the Fock space, and study the action of the Virasoro generators LnL_n. We calculate explicitly the matrix elements of LnL_n with respect to the Jack-basis. A combinatorial procedure which produces these matrix elements is conjectured. As a limiting case of the formula, we obtain a Pieri-type formula which represents a product of a power sum and a Jack symmetric function as a sum of Jack symmetric functions. Also, a similar expansion was found for the case when we differentiate the Jack symmetric functions with respect to power sums. As an application of our Jack-basis representation, a new diagrammatic interpretation is presented, why the singular vectors of the Virasoro algebra are proportional to the Jack symmetric functions with rectangular diagrams. We also propose a natural normalization of the singular vectors in the Verma module, and determine the coefficients which appear after bosonization in front of the Jack symmetric functions.Comment: 23 pages, references adde

    Dynamical Correlation Functions and Finite-size Scaling in Ruijsenaars-Schneider Model

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    The trigonometric Ruijsenaars-Schneider model is diagonalized by means of the Macdonald symmetric functions. We evaluate the dynamical density-density correlation function and the one-particle retarded Green function as well as their thermodynamic limit. Based on these results and finite-size scaling analysis, we show that the low-energy behavior of the model is described by the C=1C=1 Gaussian conformal field theory under a new fractional selection rule for the quantum numbers labeling the critical exponents.Comment: 27 pages, PS file, to be published in Nucl.Phys.

    Electron Addition Spectrum in the Supersymmetric t-J Model with Inverse-Square Interaction

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    The electron addition spectrum A^+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r^2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A^+(k,omega) has a simple analytic form with contributions from one spinon, one holon and one antiholon all of which obey fractional statistics. The upper edge of A^+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.Comment: 5 pages, 1 figure, accepted for publication in Phys. Rev. Let

    Exact operator solution of the Calogero-Sutherland model

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    The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.Comment: 35 pages, LaTeX2e with amslate

    Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial

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    Applying a method developed by Takamura and Takano for the nonsymmetric Jack polynomial, we present the Rodrigues formula for the nonsymmetric multivariable Hermite polynomial.Comment: 5 pages, LaTe
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