831 research outputs found
Integrable coupling in a model for Josephson tunneling between non-identical BCS systems
We extend a recent construction for an integrable model describing Josephson
tunneling between identical BCS systems to the case where the BCS systems have
different single particle energy levels. The exact solution of the generalized
model is obtained through the Bethe ansatz.Comment: 8 pages, latex, to appear in edition of Int. J. Mod. Phys. B
commemorating the 70th birthday of F.Y. W
Exact form factors for the Josephson tunneling current and relative particle number fluctuations in a model of two coupled Bose-Einstein condensates
Form factors are derived for a model describing the coherent Josephson
tunneling between two coupled Bose-Einstein condensates. This is achieved by
studying the exact solution of the model in the framework of the algebraic
Bethe ansatz. In this approach the form factors are expressed through
determinant representations which are functions of the roots of the Bethe
ansatz equations.Comment: 11 pages, latex, no figures, final version to appear in Lett. Math.
Phy
Exact solvability in contemporary physics
We review the theory for exactly solving quantum Hamiltonian systems through
the algebraic Bethe ansatz. We also demonstrate how this theory applies to
current studies in Bose-Einstein condensation and metallic grains which are of
nanoscale size.Comment: 23 pages, no figures, to appear in ``Classical and Quantum Nonlinear
Integrable Systems'' ed. A. Kund
Some spectral equivalences between Schrodinger operators
Spectral equivalences of the quasi-exactly solvable sectors of two classes of
Schrodinger operators are established, using Gaudin-type Bethe ansatz
equations. In some instances the results can be extended leading to full
isospectrality. In this manner we obtain equivalences between PT-symmetric
problems and Hermitian problems. We also find equivalences between some classes
of Hermitian operators.Comment: 14 page
Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation
Quantum doubles of finite group algebras form a class of quasi-triangular
Hopf algebras which algebraically solve the Yang--Baxter equation. Each
representation of the quantum double then gives a matrix solution of the
Yang--Baxter equation. Such solutions do not depend on a spectral parameter,
and to date there has been little investigation into extending these solutions
such that they do depend on a spectral parameter. Here we first explicitly
construct the matrix elements of the generators for all irreducible
representations of quantum doubles of the dihedral groups . These results
may be used to determine constant solutions of the Yang--Baxter equation. We
then discuss Baxterisation ans\"atze to obtain solutions of the Yang--Baxter
equation with spectral parameter and give several examples, including a new
21-vertex model. We also describe this approach in terms of minimal-dimensional
representations of the quantum doubles of the alternating group and the
symmetric group .Comment: 19 pages, no figures, changed introduction, added reference
The two-site Bose--Hubbard model
The two-site Bose--Hubbard model is a simple model used to study Josephson
tunneling between two Bose--Einstein condensates. In this work we give an
overview of some mathematical aspects of this model. Using a classical
analysis, we study the equations of motion and the level curves of the
Hamiltonian. Then, the quantum dynamics of the model is investigated using
direct diagonalisation of the Hamiltonian. In both of these analyses, the
existence of a threshold coupling between a delocalised and a self-trapped
phase is evident, in qualitative agreement with experiments. We end with a
discussion of the exact solvability of the model via the algebraic Bethe
ansatz.Comment: 10 pages, 5 figures, submitted for publication in Annales Henri
Poincar
Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras
The Perk--Schultz model may be expressed in terms of the solution of the
Yang--Baxter equation associated with the fundamental representation of the
untwisted affine extension of the general linear quantum superalgebra
, with a multiparametric co-product action as given by
Reshetikhin. Here we present analogous explicit expressions for solutions of
the Yang-Baxter equation associated with the fundamental representations of the
twisted and untwisted affine extensions of the orthosymplectic quantum
superalgebras . In this manner we obtain generalisations of the
Perk--Schultz model.Comment: 10 pages, 2 figure
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