748 research outputs found
Irreducible representations of deformed oscillator algebra and q-special functions
Different generators of a deformed oscillator algebra give rise to
one-parameter families of -exponential functions and -Hermite polynomials
related by generating functions. Connections of the Stieltjes and Hamburger
classical moment problems with the corresponding resolution of unity for the
-coherent states and with 'coordinate' operators - Jacobi matrices, are also
pointed out.Comment: Contribution to the workshop IWCQIS-96 (JINR, Dubna
Quantum resolution of the nonlinear super-Schrodinger equation
We introduce a Z_2-graded version of the nonlinear Schrodinger equation that
includes one fermion and one boson at the same time. This equation is shown to
possess a supersymmetry which proves to be itself part of a super-Yangian
symmetry based on gl(1|1). The solution exhibits a super version form of the
classical Rosales solution. Then, we second quantize these results, and give a
Lax pair formulation (based on gl(2|1)) for the model.Comment: 20 pages, no figur
Deformation of orthosymplectic Lie superalgebra osp(1|2)
Triangular deformation of the orthosymplectic Lie superalgebra osp(1|4) is
defined by chains of twists. Corresponding classical r-matrix is obtained by a
contraction procedure from the trigonometric r-matrix. The carrier space of the
constant r-matrix is the Borel subalgebra.Comment: LaTeX, 8 page
Jordanian deformation of the open XXX-spin chain
The general solution to the reflection equation associated with the jordanian
deformation of the SL(2) invariant Yang R-matrix is found. The same K-matrix is
obtained by the special scaling limit of the XXZ-model with general boundary
conditions. The Hamiltonian with the boundary terms is explicitly derived
according to the Sklyanin formalism. We discuss the structure of the spectrum
of the deformed XXX-model and its dependence on the boundary conditions.Comment: 13 pages; typos correcte
Twist Deformation of the rank one Lie Superalgebra
The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie
superalgebra . The twist element is the same as for the Lie
algebra due to the embedding of the into the superalgebra .
The R-matrix has the direct sum structure in the irreducible representations of
. The dual quantum group is defined using the FRT-formalism. It
includes the Jordanian quantum group as subalgebra and Grassmann
generators as well.Comment: LaTeX, 9 page
Algebraic Bethe ansatz for the gl(12) generalized model II: the three gradings
The algebraic Bethe ansatz can be performed rather abstractly for whole
classes of models sharing the same -matrix, the only prerequisite being the
existence of an appropriate pseudo vacuum state. Here we perform the algebraic
Bethe ansatz for all models with , rational, gl(12)-invariant
-matrix and all three possibilities of choosing the grading. Our Bethe
ansatz solution applies, for instance, to the supersymmetric t-J model, the
supersymmetric model and a number of interesting impurity models. It may be
extended to obtain the quantum transfer matrix spectrum for this class of
models. The properties of a specific model enter the Bethe ansatz solution
(i.e. the expression for the transfer matrix eigenvalue and the Bethe ansatz
equations) through the three pseudo vacuum eigenvalues of the diagonal elements
of the monodromy matrix which in this context are called the parameters of the
model.Comment: paragraph added in section 3, reference added, version to appear in
J.Phys.
Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)]
There being no precise definition of the quantum integrability, the
separability of variables can serve as its practical substitute. For any
quantum integrable model generated by the Yangian Y[sl(3)] the canonical
coordinates and the conjugated operators are constructed which satisfy the
``quantum characteristic equation'' (quantum counterpart of the spectral
algebraic curve for the L operator). The coordinates constructed provide a
local separation of variables. The conditions are enlisted which are necessary
for the global separation of variables to take place.Comment: 15 page
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