268 research outputs found
Planar Harmonic Polynomials of Type B
The hyperoctahedral group is the Weyl group of type B and is associated with
a two-parameter family of differential-difference operators T_i, i=1,..,N (the
dimension of the underlying Euclidean space). These operators are analogous to
partial derivative operators. This paper finds all the polynomials in N
variables which are annihilated by the sum of the squares (T_1)^2+(T_2)^2 and
by all T_i for i>2 (harmonic). They are given explicitly in terms of a novel
basis of polynomials, defined by generating functions. The harmonic polynomials
can be used to find wave functions for the quantum many-body spin Calogero
model.Comment: 17 pages, LaTe
Vector valued Macdonald polynomials
This paper defines and investigates nonsymmetric Macdonald polynomials with
values in an irreducible module of the Hecke algebra of type . These
polynomials appear as simultaneous eigenfunctions of Cherednik operators.
Several objects and properties are analyzed, such as the canonical bilinear
form which pairs polynomials with those arising from reciprocals of the
original parameters, and the symmetrization of the Macdonald polynomials. The
main tool of the study is the Yang-Baxter graph. We show that these Macdonald
polynomials can be easily computed following this graph. We give also an
interpretation of the symmetrization and the bilinear forms applied to the
Macdonald polynomials in terms of the Yang-Baxter graph.Comment: 85 pages, 5 figure
Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model
We study the hole propagator of the Calogero-Sutherland model with SU(2)
internal symmetry. We obtain the exact expression for arbitrary non-negative
integer coupling parameter and prove the conjecture proposed by one of
the authors. Our method is based on the theory of the Jack polynomials with a
prescribed symmetry.Comment: 12 pages, REVTEX, 1 eps figur
On Some One-Parameter Families of Three-Body Problems in One Dimension: Exchange Operator Formalism in Polar Coordinates and Scattering Properties
We apply the exchange operator formalism in polar coordinates to a
one-parameter family of three-body problems in one dimension and prove the
integrability of the model both with and without the oscillator potential. We
also present exact scattering solution of a new family of three-body problems
in one dimension.Comment: 10 pages, LaTeX, no figur
Supertraces on the algebra of observables of the rational Calogero model based on the classical root system
A complete set of supertraces on the algebras of observables of the rational
Calogero models with harmonic interaction based on the classical root systems
of B_N, C_N and D_N types is found. These results extend the results known for
the case A_N. It is shown that there exist Q independent supertraces where
Q(B_N)=Q(C_N) is a number of partitions of N into a sum of positive integers
and Q(D_N) is a number of partitions of N into a sum of positive integers with
even number of even integers.Comment: 10 pages, LATE
Depositional age and exhumation of Tethyan Sedimentary rocks intruded by Oligo-Miocene granite
Abstract HKT-ISTP 2013
A
Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics
We study self-adjoint operators defined by factorizing second order
differential operators in first order ones. We discuss examples where such
factorizations introduce singular interactions into simple quantum mechanical
models like the harmonic oscillator or the free particle on the circle. The
generalization of these examples to the many-body case yields quantum models of
distinguishable and interacting particles in one dimensions which can be solved
explicitly and by simple means. Our considerations lead us to a simple method
to construct exactly solvable quantum many-body systems of Calogero-Sutherland
type.Comment: 17 pages, LaTe
A Spectral Method for Elliptic Equations: The Neumann Problem
Let be an open, simply connected, and bounded region in
, , and assume its boundary is smooth.
Consider solving an elliptic partial differential equation over with a Neumann boundary condition. The problem is converted
to an equivalent elliptic problem over the unit ball , and then a spectral
Galerkin method is used to create a convergent sequence of multivariate
polynomials of degree that is convergent to . The
transformation from to requires a special analytical calculation
for its implementation. With sufficiently smooth problem parameters, the method
is shown to be rapidly convergent. For
and assuming is a boundary, the convergence of
to zero is faster than any power of .
Numerical examples in and show experimentally
an exponential rate of convergence.Comment: 23 pages, 11 figure
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