59 research outputs found
Ab Initio Calculations of the Spin-Half XY Model
In this article, the correlated basis-function (CBF) method is applied for
the first time to the quantum spin-half {\it XY} model on the linear chain, the
square lattice, and the simple cubic lattice. In this treatment of the quantum
spin-half {\it XY} model a Jastrow ansatz is utilised to approximate the
ground-state wave function. Results for the ground-state energy and the
sublattice magnetisation are presented, and evidence that the CBF detects the
quantum phase transition point in this model is also presented. The CBF results
are compared to previous coupled cluster method (CCM) results for the spin-half
{\it XY} model, and the two formalisms are then compared and contrasted.Comment: 10 pages, 3 figure
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
Multiple Thresholds in a Model System of Noisy Ion Channels
Voltage-activated ion channels vary randomly between open and closed states,
influenced by the membrane potential and other factors. Signal transduction is
enhanced by noise in a simple ion channel model. The enhancement occurs in a
finite range of signals; the range can be extended using populations of
channels. The range increases more rapidly in multiple-threshold channel
populations than in single-threshold populations. The diversity of ion channels
may thus be present as a strategy to reduce the metabolic costs of handling a
broad class of electrochemical signals.Comment: REVTeX 4, 5 pages, 4 figures; added paragrap
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
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
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
Jastrow-type calculations of one-nucleon removal reactions on open - shell nuclei
Single-particle overlap functions and spectroscopic factors are calculated on
the basis of Jastrow-type one-body density matrices of open-shell nuclei
constructed by using a factor cluster expansion. The calculations use the
relationship between the overlap functions corresponding to bound states of the
-particle system and the one-body density matrix for the ground state of
the -particle system. In this work we extend our previous analyses of
reactions on closed-shell nuclei by using the resulting overlap functions for
the description of the cross sections of reactions on the open -
shell nuclei Mg, Si and S and of S
reaction. The relative role of both shell structure and short-range
correlations incorporated in the correlation approach on the spectroscopic
factors and the reaction cross sections is pointed out.Comment: 11 pages, 5 figures, to be published in Phys. Rev.
Momentum distributions in ^3He-^4He liquid mixtures
We present variational calculations of the one-body density matrices and
momentum distributions for ^3He-^4He mixtures in the zero temperature limit, in
the framework of the correlated basis functions theory. The ground-state wave
function contains two- and three-body correlations and the matrix elements are
computed by (Fermi)Hypernetted Chain techniques. The dependence on the ^3He
concentration (x_3) of the ^4He condensate fraction and of the
^3He pole strength (Z_F) is studied along the P=0 isobar. At low ^3He
concentration, the computed ^4He condensate fraction is not significantly
affected by the ^3He statistics. Despite of the low x_3 values, Z_F is found to
be quite smaller than that of the corresponding pure ^3He because of the strong
^3He-^4He correlations and of the overall, large total density \rho. A small
increase of along x_3 is found, which is mainly due to the decrease
of \rho respect to the pure ^4He phase.Comment: 23 pages, 7 postscript figures, Revte
Effects of Short Range Correlations on Ca Isotopes
The effect of Short Range Correlations (SRC) on Ca isotopes is studied using
a simple phenomenological model. Theoretical expressions for the charge
(proton) form factors, densities and moments of Ca nuclei are derived. The role
of SRC in reproducing the empirical data for the charge density differences is
examined. Their influence on the depletion of the nuclear Fermi surface is
studied and the fractional occupation probabilities of the shell model orbits
of Ca nuclei are calculated. The variation of SRC as function of the mass
number is also discussed.Comment: 11 pages (RevTex), 6 Postscript figures available upon request at
[email protected] Physical Review C in prin
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