217 research outputs found
Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation
A method is proposed for a self-consistent evaluation of the coupling
constant in the Gross-Pitaevskii equation without involving a pseudopotential
replacement. A renormalization of the coupling constant occurs due to medium
effects and the trapping potential, e.g. in quasi-1D or quasi-2D systems. It is
shown that a simplified version of the Hartree-Fock-Bogoliubov approximation
leads to a variational problem for both the condensate and a two-body wave
function describing the behaviour of a pair of bosons in the Bose-Einstein
condensate. The resulting coupled equations are free of unphysical divergences.
Particular cases of this scheme that admit analytical estimations are
considered and compared to the literature. In addition to the well-known cases
of low-dimensional trapping, cross-over regimes can be studied. The values of
the kinetic, interaction, external, and release energies in low dimensions are
also evaluated and contributions due to short-range correlations are found to
be substantial.Comment: 15 pages, ReVTEX, no figure
Hidden Symmetries and their Consequences in Cubic Perovskites
The five-band Hubbard model for a band with one electron per site is a
model which has very interesting properties when the relevant ions are located
at sites with high (e. g. cubic) symmetry. In that case, if the crystal field
splitting is large one may consider excitations confined to the lowest
threefold degenerate orbital states. When the electron hopping matrix
element () is much smaller than the on-site Coulomb interaction energy
(), the Hubbard model can be mapped onto the well-known effective
Hamiltonian (at order ) derived by Kugel and Khomskii (KK). Recently
we have shown that the KK Hamiltonian does not support long range spin order at
any nonzero temperature due to several novel hidden symmetries that it
possesses. Here we extend our theory to show that these symmetries also apply
to the underlying three-band Hubbard model. Using these symmetries we develop a
rigorous Mermin-Wagner construction, which shows that the three-band Hubbard
model does not support spontaneous long-range spin order at any nonzero
temperature and at any order in -- despite the three-dimensional lattice
structure. Introduction of spin-orbit coupling does allow spin ordering, but
even then the excitation spectrum is gapless due to a subtle continuous
symmetry. Finally we showed that these hidden symmetries dramatically simplify
the numerical exact diagonalization studies of finite clusters.Comment: 26 pages, 3 figures, 520 KB, submitted Phys. Rev.
The ground state energy of the weakly interacting Bose gas at high density
We prove the Lee-Huang-Yang formula for the ground state energy of the 3D
Bose gas with repulsive interactions described by the exponential function, in
a simultaneous limit of weak coupling and high density. In particular, we show
that the Bogoliubov approximation is exact in an appropriate parameter regime,
as far as the ground state energy is concerned.Comment: RevTeX4, 16 page
Non Local Theories: New Rules for Old Diagrams
We show that a general variant of the Wick theorems can be used to reduce the
time ordered products in the Gell-Mann & Low formula for a certain class on non
local quantum field theories, including the case where the interaction
Lagrangian is defined in terms of twisted products.
The only necessary modification is the replacement of the
Stueckelberg-Feynman propagator by the general propagator (the ``contractor''
of Denk and Schweda)
D(y-y';tau-tau')= - i
(Delta_+(y-y')theta(tau-tau')+Delta_+(y'-y)theta(tau'-tau)), where the
violations of locality and causality are represented by the dependence of
tau,tau' on other points, besides those involved in the contraction. This leads
naturally to a diagrammatic expansion of the Gell-Mann & Low formula, in terms
of the same diagrams as in the local case, the only necessary modification
concerning the Feynman rules. The ordinary local theory is easily recovered as
a special case, and there is a one-to-one correspondence between the local and
non local contributions corresponding to the same diagrams, which is preserved
while performing the large scale limit of the theory.Comment: LaTeX, 14 pages, 1 figure. Uses hyperref. Symmetry factors added;
minor changes in the expositio
Condensate Oscillations, Kinetic Equations and Two-Fluid Hydrodynamics in a Bose Gas
This is based on 4 lectures given at the 13th Australian Physics Summer
School, Australia National University, Canberra, Jan 17-28, 2000. The main
topic is the theory of collective modes in a trapped Bose gas at finite
temperatures. A generalized Gross-Pitaevskii equation is derived at finite
temperatures, which is used to discuss a new mechanism for damping in the
collisionless region arising from interactions with a static thermal cloud of
non-condensate atoms. Next, introducing a kinetic equation for the thermal
cloud, we derive two-fluid equations of motion for the condensate and
non-condensate components in the collision-dominated hydrodynamic region. We
show that these are precisely the equivalent of the Landau two-fluid equations
in the limit that the two components are in diffusive local equilibrium.
However, our equations also predict the existence of a new zero frequency
relaxational mode, in addition to the usual Landau hydrodynamic modes (such as
first and second sound). The special importance and simplicity of two-fluid
hydrodynamics is stressed.Comment: 50 pages, 7 figures; To appear in "Proceedings of the 13th Physics
Summer S chool: Bose-Einstein Condensation", eds. C.M.Savage and M.Das (World
Scientific, 2000
Ground state properties and excitation spectra of non-Galilean invariant interacting Bose systems
We study the ground state properties and the excitation spectrum of bosons
which, in addition to a short-range repulsive two body potential, interact
through the exchange of some dispersionless bosonic modes. The latter induces a
time dependent (retarded) boson-boson interaction which is attractive in the
static limit. Moreover the coupling with dispersionless modes introduces a
reference frame for the moving boson system and hence breaks the Galilean
invariance of this system. The ground state of such a system is depleted {\it
linearly} in the boson density due to the zero point fluctuations driven by the
retarded part of the interaction. Both quasiparticle (microscopic) and
compressional (macroscopic) sound velocities of the system are studied. The
microscopic sound velocity is calculated up the second order in the effective
two body interaction in a perturbative treatment, similar to that of Beliaev
for the dilute weakly interacting Bose gas. The hydrodynamic equations are used
to obtain the macroscopic sound velocity. We show that these velocities are
identical within our perturbative approach. We present analytical results for
them in terms of two dimensional parameters -- an effective interaction
strength and an adiabaticity parameter -- which characterize the system. We
find that due the presence of several competing effects, which determine the
speed of the sound of the system, three qualitatively different regimes can be
in principle realized in the parameter space and discuss them on physical
grounds.Comment: 6 pages, 2 figures, to appear in Phys. Rev.
The fate of phonons in freely expanding Bose-Einstein condensates
Phonon-like excitations can be imprinted into a trapped Bose-Einstein
condensate of cold atoms using light scattering. If the condensate is suddenly
let to freely expand, the initial phonons lose their collective character by
transferring their energy and momentum to the motion of individual atoms. The
basic mechanisms of this evaporation process are investigated by using the
Gross-Pitaevskii theory and dynamically rescaled Bogoliubov equations.
Different regimes of evaporation are shown to occur depending on the phonon
wavelength. Distinctive signatures of the evaporated phonons are visible in the
density distribution of the expanded gas, thus providing a new type of
spectroscopy of Bogoliubov excitations.Comment: 13 pages, 16 figure
The generalized Fenyes-Nelson model for free scalar field theory
The generalized Fenyes--Nelson model of quantum mechanics is applied to the
free scalar field. The resulting Markov field is equivalent to the Euclidean
Markov field with the times scaled by a common factor which depends on the
diffusion parameter. This result is consistent between Guerra's earlier work on
stochastic quantization of scalar fields. It suggests a deep connection between
Euclidean field theory and the stochastic interpretation of quantum mechanics.
The question of Lorentz covariance is also discussed.Comment: 6 page
Time evolution of correlation functions and thermalization
We investigate the time evolution of a classical ensemble of isolated
periodic chains of O(N)-symmetric anharmonic oscillators. Our method is based
on an exact evolution equation for the time dependence of correlation
functions. We discuss its solutions in an approximation which retains all
contributions in next-to-leading order in a 1/N expansion and preserves time
reflection symmetry. We observe effective irreversibility and approximate
thermalization. At large time the system approaches stationary solutions in the
vicinity of, but not identical to, thermal equilibrium. The ensemble therefore
retains some memory of the initial condition beyond the conserved total energy.
Such a behavior with incomplete thermalization is referred to as "mesoscopic
dynamics". It is expected for systems in a small volume. Surprisingly, we find
that the nonthermal asymptotic stationary solutions do not change for large
volume. This raises questions on Boltzmann's conjecture that macroscopic
isolated systems thermalize.Comment: 40 pages, 9 figure
The Second Order Upper Bound for the Ground Energy of a Bose Gas
Consider bosons in a finite box
interacting via a two-body smooth repulsive short range potential. We construct
a variational state which gives the following upper bound on the ground state
energy per particle where is the scattering
length of the potential. Previously, an upper bound of the form
for some constant was obtained in \cite{ESY}. Our result proves the
upper bound of the the prediction by Lee-Yang \cite{LYang} and Lee-Huang-Yang
\cite{LHY}.Comment: 62 pages, no figure
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