1,278 research outputs found
Irreducible Modules of Finite Dimensional Quantum Algebras of type A at Roots of Unity
Specializing properly the parameters contained in the maximal cyclic
representation of the non-restricted A-type quantum algebra at roots of unity,
we find the unique primitive vector in it. We show that the submodule generated
by the primitive vector can be identified with an irreducble highest weight
module of the finite dimensional A-type quantum algebra which is defined as the
subalgebra of the restricted quantum algebra at roots of unity.Comment: LaTeX(2e), 17 page
Asymptotic analysis and spectrum of three anyons
The spectrum of anyons confined in harmonic oscillator potential shows both
linear and nonlinear dependence on the statistical parameter. While the
existence of exact linear solutions have been shown analytically, the nonlinear
dependence has been arrived at by numerical and/or perturbative methods. We
develop a method which shows the possibility of nonlinearly interpolating
spectrum. To be specific we analyse the eigenvalue equation in various
asymptotic regions for the three anyon problem.Comment: 28 pages, LaTeX, 2 Figure
Classical and Quantum Mechanics of Anyons
We review aspects of classical and quantum mechanics of many anyons confined
in an oscillator potential. The quantum mechanics of many anyons is complicated
due to the occurrence of multivalued wavefunctions. Nevertheless there exists,
for arbitrary number of anyons, a subset of exact solutions which may be
interpreted as the breathing modes or equivalently collective modes of the full
system. Choosing the three-anyon system as an example, we also discuss the
anatomy of the so called ``missing'' states which are in fact known numerically
and are set apart from the known exact states by their nonlinear dependence on
the statistical parameter in the spectrum.
Though classically the equations of motion remains unchanged in the presence
of the statistical interaction, the system is non-integrable because the
configuration space is now multiply connected. In fact we show that even though
the number of constants of motion is the same as the number of degrees of
freedom the system is in general not integrable via action-angle variables.
This is probably the first known example of a many body pseudo-integrable
system. We discuss the classification of the orbits and the symmetry reduction
due to the interaction. We also sketch the application of periodic orbit theory
(POT) to many anyon systems and show the presence of eigenvalues that are
potentially non-linear as a function of the statistical parameter. Finally we
perform the semiclassical analysis of the ground state by minimizing the
Hamiltonian with fixed angular momentum and further minimization over the
quantized values of the angular momentum.Comment: 44 pages, one figure, eps file. References update
Free field realizations of the Date-Jimbo-Kashiwara-Miwa algebra
We use the description of the universal central extension of the DJKM algebra
where
given in earlier work to construct realizations of the DJKM algebra in terms of
sums of partial differential operators.Comment: arXiv admin note: substantial text overlap with arXiv:1303.697
Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation
The sine-Gordon equation is considered in the hamiltonian framework provided
by the Adler-Kostant-Symes theorem. The phase space, a finite dimensional
coadjoint orbit in the dual space \grg^* of a loop algebra \grg, is
parametrized by a finite dimensional symplectic vector space embedded into
\grg^* by a moment map. Real quasiperiodic solutions are computed in terms of
theta functions using a Liouville generating function which generates a
canonical transformation to linear coordinates on the Jacobi variety of a
suitable hyperelliptic curve.Comment: 12 pg
Classical Many-particle Clusters in Two Dimensions
We report on a study of a classical, finite system of confined particles in
two dimensions with a two-body repulsive interaction. We first develop a simple
analytical method to obtain equilibrium configurations and energies for few
particles. When the confinement is harmonic, we prove that the first transition
from a single shell occurs when the number of particles changes from five to
six. The shell structure in the case of an arbitrary number of particles is
shown to be independent of the strength of the interaction but dependent only
on its functional form. It is also independent of the magnetic field strength
when included. We further study the effect of the functional form of the
confinement potential on the shell structure. Finally we report some
interesting results when a three-body interaction is included, albeit in a
particular model.Comment: Minor corrections, a few references added. To appear in J. Phys:
Condensed Matte
Vertex Operator Representation of the Soliton Tau Functions in the Toda Models by Dressing Transformations
We study the relation between the group-algebraic approach and the dressing
symmetry one to the soliton solutions of the Toda field theory in
1+1 dimensions. Originally solitons in the affine Toda models has been found by
Olive, Turok and Underwood. Single solitons are created by exponentials of
elements which ad-diagonalize the principal Heisenberg subalgebra.
Alternatively Babelon and Bernard exploited the dressing symmetry to reproduce
the known expressions for the fundamental tau functions in the sine-Gordon
model. In this paper we show the equivalence between these two methods to
construct solitons in the Toda models.Comment: 35 pages, LaTe
Quantum suppression of the generic chaotic behavior close to cosmological singularities
In classical general relativity, the generic approach to the initial
singularity is very complicated as exemplified by the chaos of the Bianchi IX
model which displays the generic local evolution close to a singularity.
Quantum gravity effects can potentially change the behavior and lead to a
simpler initial state. This is verified here in the context of loop quantum
gravity, using methods of loop quantum cosmology: the chaotic behavior stops
once quantum effects become important. This is consistent with the discrete
structure of space predicted by loop quantum gravity.Comment: revtex4, 4 pages, 5 figures. Published version. Title and abstract
changed to match with the published version and Other minor changes.
Conclusions unchange
Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies
Basic representations of A_{2l}^(2) and D_{l+1}^(2) are studied. The weight
vectors are represented in terms of Schur's -functions. The method to get
the polynomial solutions to the reduced BKP hierarchies is shown to be
equivalent to a certain rule in Maya game.Comment: January 1994, 11 page
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