304 research outputs found

### Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model

We present an algebraic construction of the orthogonal eigenfunctions of the
supersymmetric extension of the rational Calogero-Moser-Sutherland model with
harmonic confinement. These eigenfunctions are the superspace extension of the
generalized Hermite (or Hi-Jack) polynomials. The conserved quantities of the
rational supersymmetric model are related to their trigonometric relatives
through a similarity transformation. This leads to a simple expression between
the corresponding eigenfunctions: the generalized Hermite superpolynomials are
written as a differential operator acting on the corresponding Jack
superpolynomials. As an aside, the maximal superintegrability of the
supersymmetric rational Calogero-Moser-Sutherland model is demonstrated.Comment: Latex 2e, shortened version, one reference added, 18 page

### A CA Hybrid of the Slow-to-Start and the Optimal Velocity Models and its Flow-Density Relation

The s2s-OVCA is a cellular automaton (CA) hybrid of the optimal velocity (OV)
model and the slow-to-start (s2s) model, which is introduced in the framework
of the ultradiscretization method. Inverse ultradiscretization as well as the
time continuous limit, which lead the s2s-OVCA to an integral-differential
equation, are presented. Several traffic phases such as a free flow as well as
slow flows corresponding to multiple metastable states are observed in the
flow-density relations of the s2s-OVCA. Based on the properties of the
stationary flow of the s2s-OVCA, the formulas for the flow-density relations
are derived

### Orthogonal Symmetric Polynomials Associated with the Calogero Model

The Calogero model is a one-dimensional quantum integrable system with
inverse-square long-range interactions confined in an external harmonic well.
It shares the same algebraic structure with the Sutherland model, which is also
a one-dimensional quantum integrable system with inverse-sine-square
interactions. Inspired by the Rodrigues formula for the Jack polynomials, which
form the orthogonal basis of the Sutherland model, recently found by Lapointe
and Vinet, we construct the Rodrigues formula for the Hi-Jack (hidden-Jack)
polynomials that form the orthogonal basis of the Calogero model.Comment: 12pages, LaTeX file using citesort.sty and subeqn.sty, to appear in
the proceedings of Canada-China Meeting in Mathematical Physics, Tianjin,
China, August 19--24, 1996, ed. M.-L. Ge, Y. Saint-Aubin and L. Vinet
(Springer-Verlag

### Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model

The Hi-Jack symmetric polynomials, which are associated with the simultaneous
eigenstates for the first and second conserved operators of the quantum
Calogero model, are studied. Using the algebraic properties of the Dunkl
operators for the model, we derive the Rodrigues formula for the Hi-Jack
symmetric polynomials. Some properties of the Hi-Jack polynomials and the
relationships with the Jack symmetric polynomials and with the basis given by
the QISM approach are presented. The Hi-Jack symmetric polynomials are strong
candidates for the orthogonal basis of the quantum Calogero model.Comment: 17 pages, LaTeX file using jpsj.sty (ver. 0.8), cite.sty,
subeqna.sty, subeqn.sty, jpsjbs1.sty and jpsjbs2.sty (all included.) You can
get all the macros from ftp.u-tokyo.ac.jp/pub/SOCIETY/JPSJ

### The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles

From random matrix theory it is known that for special values of the coupling
constant the Calogero-Moser (CM) equation system is nothing but the radial part
of a generalized harmonic oscillator Schroedinger equation. This allows an
immediate construction of the solutions by means of a Rodriguez relation. The
results are easily generalized to arbitrary values of the coupling constant. By
this the CM equations become nearly trivial.
As an application an expansion for in terms of eigenfunctions of
the CM equation system is obtained, where X and Y are matrices taken from one
of the Gaussian ensembles, and the brackets denote an average over the angular
variables.Comment: accepted by J. Phys.

### Common Algebraic Structure for the Calogero-Sutherland Models

We investigate common algebraic structure for the rational and trigonometric
Calogero-Sutherland models by using the exchange-operator formalism. We show
that the set of the Jack polynomials whose arguments are Dunkl-type operators
provides an orthogonal basis for the rational case.Comment: 7 pages, LaTeX, no figures, some text and references added, minor
misprints correcte

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