12 research outputs found
Finite-temperature simulations of the scissors mode in Bose-Einstein condensed gases
The dynamics of a trapped Bose-condensed gas at finite temperatures is
described by a generalized Gross-Pitaevskii equation for the condensate order
parameter and a semi-classical kinetic equation for the thermal cloud, solved
using -body simulations. The two components are coupled by mean fields as
well as collisional processes that transfer atoms between the two. We use this
scheme to investigate scissors modes in anisotropic traps as a function of
temperature. Frequency shifts and damping rates of the condensate mode are
extracted, and are found to be in good agreement with recent experiments.Comment: 4 pages, 3 figure
Landau-Khalatnikov two-fluid hydrodynamics of a trapped Bose gas
Starting from the quantum kinetic equation for the non-condensate atoms and
the generalized Gross-Pitaevskii equation for the condensate, we derive the
two-fluid hydrodynamic equations of a trapped Bose gas at finite temperatures.
We follow the standard Chapman-Enskog procedure, starting from a solution of
the kinetic equation corresponding to the complete local equilibrium between
the condensate and the non-condensate components. Our hydrodynamic equations
are shown to reduce to a form identical to the well-known Landau-Khalatnikov
two-fluid equations, with hydrodynamic damping due to the deviation from local
equilibrium. The deviation from local equilibrium within the thermal cloud
gives rise to dissipation associated with shear viscosity and thermal
conduction. In addition, we show that effects due to the deviation from the
diffusive local equilibrium between the condensate and the non-condensate
(recently considered by Zaremba, Nikuni and Griffin) can be described by four
frequency-dependent second viscosity transport coefficients. We also derive
explicit formulas for all the transport coefficients. These results are used to
introduce two new characteristic relaxation times associated with hydrodynamic
damping. These relaxation times give the rate at which local equilibrium is
reached and hence determine whether one is in the two-fluid hydrodynamic
region.Comment: 26 pages, 3 postscript figures, submitted to PR
Quantum Kinetic Theory of BEC Lattice Gas:Boltzmann Equations from 2PI-CTP Effective Action
We continue our earlier work [Ana Maria Rey, B. L. Hu, Esteban Calzetta,
Albert Roura and Charles W. Clark, Phys. Rev. A 69, 033610 (2004)] on the
nonequilibrium dynamics of a Bose Einstein condensate (BEC) selectively loaded
into every third site of a one-dimensional optical lattice. From the
two-particle irreducible (2PI) closed-time-path (CTP) effective action for the
Bose- Hubbard Hamiltonian, we show how to obtain the Kadanoff-Baym equations of
quantum kinetic theory. Using the quasiparticle approximation, we show that the
local equilibrium solutions of these equations reproduce the second- order
corrections to the self-energy originally derived by Beliaev. This work paves
the way for the use of effective action methods in the derivation of quantum
kinetic theory of many atom systems.Comment: 21 pages, 0 figures, minor editorial changes were mad
Beyond Gross-Pitaevskii Mean Field Theory
A large number of effects related to the phenomenon of Bose-Einstein
Condensation (BEC) can be understood in terms of lowest order mean field
theory, whereby the entire system is assumed to be condensed, with thermal and
quantum fluctuations completely ignored. Such a treatment leads to the
Gross-Pitaevskii Equation (GPE) used extensively throughout this book. Although
this theory works remarkably well for a broad range of experimental parameters,
a more complete treatment is required for understanding various experiments,
including experiments with solitons and vortices. Such treatments should
include the dynamical coupling of the condensate to the thermal cloud, the
effect of dimensionality, the role of quantum fluctuations, and should also
describe the critical regime, including the process of condensate formation.
The aim of this Chapter is to give a brief but insightful overview of various
recent theories, which extend beyond the GPE. To keep the discussion brief,
only the main notions and conclusions will be presented. This Chapter
generalizes the presentation of Chapter 1, by explicitly maintaining
fluctuations around the condensate order parameter. While the theoretical
arguments outlined here are generic, the emphasis is on approaches suitable for
describing single weakly-interacting atomic Bose gases in harmonic traps.
Interesting effects arising when condensates are trapped in double-well
potentials and optical lattices, as well as the cases of spinor condensates,
and atomic-molecular coupling, along with the modified or alternative theories
needed to describe them, will not be covered here.Comment: Review Article (19 Pages) - To appear in 'Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment', Edited by
P.G. Kevrekidis, D.J. Frantzeskakis and R. Carretero-Gonzalez (Springer
Verlag
Finite Temperature Models of Bose-Einstein Condensation
The theoretical description of trapped weakly-interacting Bose-Einstein
condensates is characterized by a large number of seemingly very different
approaches which have been developed over the course of time by researchers
with very distinct backgrounds. Newcomers to this field, experimentalists and
young researchers all face a considerable challenge in navigating through the
`maze' of abundant theoretical models, and simple correspondences between
existing approaches are not always very transparent. This Tutorial provides a
generic introduction to such theories, in an attempt to single out common
features and deficiencies of certain `classes of approaches' identified by
their physical content, rather than their particular mathematical
implementation.
This Tutorial is structured in a manner accessible to a non-specialist with a
good working knowledge of quantum mechanics. Although some familiarity with
concepts of quantum field theory would be an advantage, key notions such as the
occupation number representation of second quantization are nonetheless briefly
reviewed. Following a general introduction, the complexity of models is
gradually built up, starting from the basic zero-temperature formalism of the
Gross-Pitaevskii equation. This structure enables readers to probe different
levels of theoretical developments (mean-field, number-conserving and
stochastic) according to their particular needs. In addition to its `training
element', we hope that this Tutorial will prove useful to active researchers in
this field, both in terms of the correspondences made between different
theoretical models, and as a source of reference for existing and developing
finite-temperature theoretical models.Comment: Detailed Review Article on finite temperature theoretical techniques
for studying weakly-interacting atomic Bose-Einstein condensates written at
an elementary level suitable for non-experts in this area (e.g. starting PhD
students). Now includes table of content