79 research outputs found
Ab Initio Treatments of the Ising Model in a Transverse Field
In this article, new results are presented for the zero-temperature
ground-state properties of the spin-half transverse Ising model on various
lattices using three different approximate techniques. These are, respectively,
the coupled cluster method, the correlated basis function method, and the
variational quantum Monte Carlo method. The methods, at different levels of
approximation, are used to study the ground-state properties of these systems,
and the results are found to be in excellent agreement both with each other and
with results of exact calculations for the linear chain and results of exact
cumulant series expansions for lattices of higher spatial dimension. The
different techniques used are compared and contrasted in the light of these
results, and the constructions of the approximate ground-state wave functions
are especially discussed.Comment: 28 Pages, 4 Figures, 1 Tabl
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
Final state effects on superfluid He in the deep inelastic regime
A study of Final State Effects (FSE) on the dynamic structure function of
superfluid He in the Gersch--Rodriguez formalism is presented. The main
ingredients needed in the calculation are the momentum distribution and the
semidiagonal two--body density matrix. The influence of these ground state
quantities on the FSE is analyzed. A variational form of is used, even
though simpler forms turn out to give accurate results if properly chosen.
Comparison to the experimental response at high momentum transfer is performed.
The predicted response is quite sensitive to slight variations on the value of
the condensate fraction, the best agreement with experiment being obtained with
. Sum rules of the FSE broadening function are also derived and
commented. Finally, it is shown that Gersch--Rodriguez theory produces results
as accurate as those coming from other more recent FSE theories.Comment: 20 pages, RevTex 3.0, 11 figures available upon request, to be appear
in Phys. Rev.
Ammonia Decomposition in the Process Chain for a Renewable Hydrogen Supply
This review article deals with the challenge to identify catalyst materials from literature studies for the ammonia decomposition reaction with potential for application in large-scale industrial processes. On the one hand, the requirements on the catalyst are quite demanding. Of central importance are the conditions for the primary reaction that have to be met by the catalyst. Likewise, the catalytic performance, i.e., an ideally quantitative conversion, and a high lifetime are critical as well as the consideration of requirements on the product properties in terms of pressure or by-products for potential follow-up processes, in this case synthesis gas applications. On the other hand, the evaluation of the multitude of literature studies poses difficulties due to significant varieties in catalytic testing protocols
Phase transition in the transverse Ising model using the extended coupled-cluster method
The phase transition present in the linear-chain and square-lattice cases of
the transverse Ising model is examined. The extended coupled cluster method
(ECCM) can describe both sides of the phase transition with a unified approach.
The correlation length and the excitation energy are determined. We demonstrate
the ability of the ECCM to use both the weak- and the strong-coupling starting
state in a unified approach for the study of critical behavior.Comment: 10 pages, 7 eps-figure
Surface Region of Superfluid Helium as an Inhomogeneous Bose-Condensed Gas
We present arguments that the low density surface region of self-bounded
superfluid He systems is an inhomogeneous dilute Bose gas, with almost all
of the atoms occupying the same single-particle state at . Numerical
evidence for this complete Bose-Einstein condensation was first given by the
many-body variational calculations of He droplets by Lewart, Pandharipande
and Pieper in 1988. We show that the low density surface region can be treated
rigorously using a generalized Gross-Pitaevskii equation for the Bose order
parameter.Comment: 4 pages, 1 Postscript figur
Quantum phase transitions and thermodynamic properties in highly anisotropic magnets
The systems exhibiting quantum phase transitions (QPT) are investigated
within the Ising model in the transverse field and Heisenberg model with
easy-plane single-site anisotropy. Near QPT a correspondence between parameters
of these models and of quantum phi^4 model is established. A scaling analysis
is performed for the ground-state properties. The influence of the external
longitudinal magnetic field on the ground-state properties is investigated, and
the corresponding magnetic susceptibility is calculated. Finite-temperature
properties are considered with the use of the scaling analysis for the
effective classical model proposed by Sachdev. Analytical results for the
ordering temperature and temperature dependences of the magnetization and
energy gap are obtained in the case of a small ground-state moment. The forms
of dependences of observable quantities on the bare splitting (or magnetic
field) and renormalized splitting turn out to be different. A comparison with
numerical calculations and experimental data on systems demonstrating magnetic
and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure
Cold Bose gases with large scattering lengths
We calculate the energy and condensate fraction for a dense system of bosons
interacting through an attractive short range interaction with positive s-wave
scattering length . At high densities, , the energy per particle,
chemical potential, and square of the sound speed are independent of the
scattering length and proportional to , as in Fermi systems.Comment: 4 pages, 3 figure
Momentum distribution of liquid helium
We have obtained the one--body density matrix and the momentum distribution
of liquid He at K from Diffusion Monte Carlo (DMC)
simulations, using trial functions optimized via the Euler Monte Carlo (EMC)
method. We find a condensate fraction smaller than in previous calculations.
Though we do not explicitly include long--range correlations in our
calculations, we get a momentum distribution at long wavelength which is
compatible with the presence of long--range correlations in the exact wave
function. We have also studied He, using fixed--node DMC, with nodes and
trial functions provided by the EMC. In particular, we analyze the momentum
distribution with respect to the discontinuity as well as the
singular behavior, at the Fermi surface. We also show that an approximate
factorization of the one-body density matrix
holds, with and respectively the density matrix of the
ideal Fermi gas and the density matrix of a Bose He.Comment: 10 pages, REVTeX, 12 figure
Description of recent large- neutron inclusive scattering data from liquid He
We report dynamical calculations for large- structure functions of liquid
He at =1.6 and 2.3 K and compare those with recent MARI data. We extend
those calculations far beyond the experimental range q\le 29\Ain in order to
study the approach of the response to its asymptotic limit for a system with
interactions having a strong short-range repulsion. We find only small
deviations from theoretical behavior, valid for smooth . We repeat an
extraction by Glyde et al of cumulant coefficients from data. We argue that
fits determine the single atom momentum distribution, but express doubt as to
the extraction of meaningful Final State Interaction parameters.Comment: 37 pages, 13 postscript fig
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