5,322 research outputs found
Excitations and S-matrix for su(3) spin chain combining and ${3^{*}}
The associated Hamiltonian for a su(3) spin chain combining and
representations is calculated. The ansatz equations for this chain
are obtained and solved in the thermodynamic limit, and the ground state and
excitations are described. Thus, relations between the number of roots and the
number of holes in each level have been found . The excited states are
characterized by means of these quantum numbers. Finally, the exact S matrix
for a state with two holes is found.Comment: 17 pages, plaintex, harvmac (to be published in J. of Phys. A
Dipolar condensates confined in a toroidal trap: ground state and vortices
We study a Bose-Einstein condensate of 52Cr atoms confined in a toroidal trap
with a variable strength of s-wave contact interactions. We analyze the effects
of the anisotropic nature of the dipolar interaction by considering the
magnetization axis to be perpendicular to the trap symmetry axis. In the
absence of a central repulsive barrier, when the trap is purely harmonic, the
effect of reducing the scattering length is a tuning of the geometry of the
system: from a pancake-shaped condensate when it is large, to a cigar-shaped
condensate for small scattering lengths. For a condensate in a toroidal trap,
the interaction in combination with the central repulsive Gaussian barrier
produces an azimuthal dependence of the particle density for a fixed radial
distance. We find that along the magnetization direction the density decreases
as the scattering length is reduced but presents two symmetric density peaks in
the perpendicular axis. For even lower values of the scattering length we
observe that the system undergoes a dipolar-induced symmetry breaking
phenomenon. The whole density becomes concentrated in one of the peaks,
resembling an origin-displaced cigar-shaped condensate. In this context we also
analyze stationary vortex states and their associated velocity field, finding
that this latter also shows a strong azimuthal dependence for small scattering
lengths. The expectation value of the angular momentum along the z direction
provides a qualitative measure of the difference between the velocity in the
different density peaks.Comment: 9 pages, 12 figure
Integrable su(3) spin chain combining different representations
The general expression for the local matrix of a quantum chain
with the site space in any representation of su(3) is obtained. This is made by
generalizing from the fundamental representation and imposing the
fulfillment of the Yang-Baxter equation. Then, a non-homogeneous spin chain
combining different representations of su(3) is solved by developing a method
inspired in the nested Bethe ansatz. The solution for the eigenvalues of the
trace of the monodromy matrix is given as two coupled Bethe equations. A
conjecture about the solution of a chain with the site states in different
representations of su(n) is presented. The thermodynamic limit of the ground
state is calculated.Comment: PlainTex harvmac, 30 pages, 7 figures, to appear in Journal of
Physics
- …