1,013 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
Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates
In this work we investigate the energy gap between the ground state and the
first excited state in a model of two single-mode Bose-Einstein condensates
coupled via Josephson tunneling. The energy gap is never zero when the
tunneling interaction is non-zero. The gap exhibits no local minimum below a
threshold coupling which separates a delocalised phase from a self-trapping
phase which occurs in the absence of the external potential. Above this
threshold point one minimum occurs close to the Josephson regime, and a set of
minima and maxima appear in the Fock regime. Analytic expressions for the
position of these minima and maxima are obtained. The connection between these
minima and maxima and the dynamics for the expectation value of the relative
number of particles is analysed in detail. We find that the dynamics of the
system changes as the coupling crosses these points.Comment: 12 pages, 5 .eps figures + 4 figs, classical analysis, perturbation
theor
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
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