862 research outputs found
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
Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
The representation theory of the Drinfeld doubles of dihedral groups is used
to solve the Yang-Baxter equation. Use of the 2-dimensional representations
recovers the six-vertex model solution. Solutions in arbitrary dimensions,
which are viewed as descendants of the six-vertex model case, are then obtained
using tensor product graph methods which were originally formulated for quantum
algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure
Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry
The exact solution for the energy spectrum of a one-dimensional Hamiltonian
with local two-site interactions and periodic boundary conditions is
determined. The two-site Hamiltonians commute with the symmetry algebra given
by the Drinfeld double D(D_3) of the dihedral group D_3. As such the model
describes local interactions between non-Abelian anyons, with fusion rules
given by the tensor product decompositions of the irreducible representations
of D(D_3). The Bethe ansatz equations which characterise the exact solution are
found through the use of functional relations satisfied by a set of mutually
commuting transfer matrices.Comment: 19 page
Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model
Lipkin model of arbitrary particle-number N is studied in terms of exact
differential-operator representation of spin-operators from which we obtain the
low-lying energy spectrum with the instanton method of quantum tunneling. Our
new observation is that the well known quantum phase transition can also occur
in the finite-N model only if N is an odd-number. We furthermore demonstrate a
new type of quantum phase transition characterized by level-crossing which is
induced by the geometric phase interference and is marvelously periodic with
respect to the coupling parameter. Finally the conventional quantum phase
transition is understood intuitively from the tunneling formulation in the
thermodynamic limit.Comment: 4 figure
Transfer matrix eigenvalues of the anisotropic multiparametric U model
A multiparametric extension of the anisotropic U model is discussed which
maintains integrability. The R-matrix solving the Yang-Baxter equation is
obtained through a twisting construction applied to the underlying Uq(sl(2|1))
superalgebraic structure which introduces the additional free parameters that
arise in the model. Three forms of Bethe ansatz solution for the transfer
matrix eigenvalues are given which we show to be equivalent.Comment: 26 pages, no figures, LaTe
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