4,997 research outputs found
Dynamical correlation functions in the Calogero-Sutherland model
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 Algebra
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 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
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
We study the conformal field theory of a free compactified boson with
radius ( 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 conformal field theory at
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 and particle with statistics .Comment: 17 page
Single particle Green's function in the Calogero-Sutherland model for rational couplings
We derive an exact expression for the single particle Green function in the
Calogero-Sutherland model for all rational values of the coupling . 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
We use the Jack symmetric functions as a basis of the Fock space, and study
the action of the Virasoro generators . We calculate explicitly the matrix
elements of 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
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
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
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
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
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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