10 research outputs found
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.
Renormalization Effects in a Dilute Bose Gas
The low-density expansion for a homogeneous interacting Bose gas at zero
temperature can be formulated as an expansion in powers of ,
where is the number density and is the S-wave scattering length.
Logarithms of appear in the coefficients of the expansion. We show
that these logarithms are determined by the renormalization properties of the
effective field theory that describes the scattering of atoms at zero density.
The leading logarithm is determined by the renormalization of the pointlike scattering amplitude.Comment: 10 pages, 1 postscript figure, LaTe
Properties of a Dilute Bose Gas near a Feshbach Resonance
In this paper, properties of a homogeneous Bose gas with a Feshbach resonance
are studied in the dilute region at zero temperature. The stationary state
contains condensations of atoms and molecules. The ratio of the molecule
density to the atom density is . There are two types of excitations,
molecular excitations and atomic excitations. Atomic excitations are gapless,
consistent with the traditional theory of a dilute Bose gas. The molecular
excitation energy is finite in the long wavelength limit as observed in recent
experiments on Rb. In addition, the decay process of the condensate is
studied. The coefficient of the three-body recombination rate is about 140
times larger than that of a Bose gas without a Feshbach resonance, in
reasonably good agreement with the experiment on Na.Comment: 11 pages, 1 figure, comparison between the calculated three-body
recombination rate and the experimental data for Na system has been adde
Variational self-consistent theory for trapped Bose gases at finite temperature
We apply the time-dependent variational principle of Balian-V\'en\'eroni to a
system of self-interacting trapped bosons at finite temperature. The method
leads to a set of coupled non-linear time dependent equations for the
condensate density, the thermal cloud and the anomalous density. We solve
numerically these equations in the static case for a harmonic trap. We analyze
the various densities as functions of the radial distance and the temperature.
We find an overall good qualitative agreement with recent experiments as well
as with the results of many theoretical groups. We also discuss the behavior of
the anomalous density at low temperatures owing to its importance to account
for many-body effects.Comment: 8 pages, 8 figure
Number--conserving model for boson pairing
An independent pair ansatz is developed for the many body wavefunction of
dilute Bose systems. The pair correlation is optimized by minimizing the
expectation value of the full hamiltonian (rather than the truncated Bogoliubov
one) providing a rigorous energy upper bound. In contrast with the Jastrow
model, hypernetted chain theory provides closed-form exactly solvable equations
for the optimized pair correlation. The model involves both condensate and
coherent pairing with number conservation and kinetic energy sum rules
satisfied exactly and the compressibility sum rule obeyed at low density. We
compute, for bulk boson matter at a given density and zero temperature, (i) the
two--body distribution function, (ii) the energy per particle, (iii) the sound
velocity, (iv) the chemical potential, (v) the momentum distribution and its
condensate fraction and (vi) the pairing function, which quantifies the ODLRO
resulting from the structural properties of the two--particle density matrix.
The connections with the low--density expansion and Bogoliubov theory are
analyzed at different density values, including the density and scattering
length regime of interest of trapped-atoms Bose--Einstein condensates.
Comparison with the available Diffusion Monte Carlo results is also made.Comment: 21 pages, 12 figure