24 research outputs found
Phase transitions in a spin-1 model with plaquette interaction on the square lattice
An extension of the Blume-Emery-Griffiths model with a plaquette four-spin interaction term, on the square lattice, is investigated by means of the cluster variation method in the square approximation. The ground state of the model, for negative plaquette interaction, exhibits several new phases, including frustrated ones. At finite temperature we obtain a quite rich phase diagram with two new phases, a ferrimagnetic and a weakly ferromagnetic one, and several multicritical points
Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap
We study the numerical resolution of the time-dependent Gross-Pitaevskii
equation, a non-linear Schroedinger equation used to simulate the dynamics of
Bose-Einstein condensates. Considering condensates trapped in harmonic
potentials, we present an efficient algorithm by making use of a spectral
Galerkin method, using a basis set of harmonic oscillator functions, and the
Gauss-Hermite quadrature. We apply this algorithm to the simulation of
condensate breathing and scissors modes.Comment: 23 pages, 5 figure
Spatial coherence and density correlations of trapped Bose gases
We study first and second order coherence of trapped dilute Bose gases using
appropriate correlation functions. Special attention is given to the discussion
of second order or density correlations. Except for a small region around the
surface of a Bose-Einstein condensate the correlations can be accurately
described as those of a locally homogeneous gas with a spatially varying
chemical potential. The degrees of first and second order coherence are
therefore functions of temperature, chemical potential, and position. The
second order correlation function is governed both by the tendency of bosonic
atoms to cluster and by a strong repulsion at small distances due to atomic
interactions. In present experiments both effects are of comparable magnitude.
Below the critical temperature the range of the bosonic correlation is affected
by the presence of collective quasi-particle excitations. The results of some
recent experiments on second and third order coherence are discussed. It is
shown that the relation between the measured quantities and the correlation
functions is much weaker than previously assumed.Comment: RevTeX, 25 pages with 7 Postscript figure
Theory of Bose-Einstein condensation in trapped gases
The phenomenon of Bose-Einstein condensation of dilute gases in traps is
reviewed from a theoretical perspective. Mean-field theory provides a framework
to understand the main features of the condensation and the role of
interactions between particles. Various properties of these systems are
discussed, including the density profiles and the energy of the ground state
configurations, the collective oscillations and the dynamics of the expansion,
the condensate fraction and the thermodynamic functions. The thermodynamic
limit exhibits a scaling behavior in the relevant length and energy scales.
Despite the dilute nature of the gases, interactions profoundly modify the
static as well as the dynamic properties of the system; the predictions of
mean-field theory are in excellent agreement with available experimental
results. Effects of superfluidity including the existence of quantized vortices
and the reduction of the moment of inertia are discussed, as well as the
consequences of coherence such as the Josephson effect and interference
phenomena. The review also assesses the accuracy and limitations of the
mean-field approach.Comment: revtex, 69 pages, 38 eps figures, new version with more references,
new figures, various changes and corrections, for publ. in Rev. Mod. Phys.,
available also at http://www-phys.science.unitn.it/bec/BEC.htm
Low Energy Excitation Spectra of Trapped Bose Condensates
We discuss our numerical studies of the low energy excitations of trapped Bose condensates using a Bogoliubov-Hartree treatment. In the zero temperature limit, the lowest few excitation frequencies calculated within the Bogoliubov approximation agree well with the experimental data. Finite temperature results obtained using the Popov approximation display qualitative differences from the experimental data close to the critical temperature region. Details of our numerical approach are presented and comparison with other results is discussed