64,236 research outputs found
An Attempt to Calculate Energy Eigenvalues in Quantum Systems of Large Sizes
We report an attempt to calculate energy eigenvalues of large quantum systems
by the diagonalization of an effectively truncated Hamiltonian matrix. For this
purpose we employ a specific way to systematically make a set of orthogonal
states from a trial wavefunction and the Hamiltonian. In comparison with the
Lanczos method, which is quite powerful if the size of the system is within the
memory capacity of computers, our method requires much less memory resources at
the cost of the extreme accuracy.
In this paper we demonstrate that our method works well in the systems of
one-dimensional frustrated spins up to 48 sites, of bosons on a chain up to 32
sites and of fermions on a ladder up to 28 sites. We will see this method
enables us to study eigenvalues of these quantum systems within reasonable
accuracy.Comment: 17pages, 4figures(eps-files
Falicov-Kimball model and the problem of electronic ferroelectricity
The density matrix renormalization group method is used to examine
possibilities of electronic ferroelectricity in the spinless Falicov-Kimball
model. The model is studied for a wide range of parameters including weak and
strong interactions as well as the symmetric and unsymmetric case. In all
examined cases the -expectation value vanishes for vanishing
hybridization , indicating that the spinless Falicov-Kimball model does not
allow for a ferroelectric ground state with a spontaneous polarization.Comment: 9 pages, 4 figures, LaTe
Normalizing the Temperature Function of Clusters of Galaxies
We re-examine the constraints which can be robustly obtained from the
observed temperature function of X-ray cluster of galaxies. The cluster mass
function has been thoroughly studied in simulations and analytically, but a
direct simulation of the temperature function is presented here for the first
time. Adaptive hydrodynamic simulations using the cosmological Moving Mesh
Hydro code of Pen (1997a) are used to calibrate the temperature function for
different popular cosmologies. Applying the new normalizations to the
present-day cluster abundances, we find for a hyperbolic universe, and for a spatially flat universe with a cosmological constant.
The simulations followed the gravitational shock heating of the gas and dark
matter, and used a crude model for potential energy injection by supernova
heating. The error bars are dominated by uncertainties in the heating/cooling
models. We present fitting formulae for the mass-temperature conversions and
cluster abundances based on these simulations.Comment: 20 pages incl 5 figures, final version for ApJ, corrected open
universe \gamma relation, results unchange
Weak Lensing as a Calibrator of the Cluster Mass-Temperature Relation
The abundance of clusters at the present epoch and weak gravitational lensing
shear both constrain roughly the same combination of the power spectrum
normalization sigma_8 and matter energy density Omega_M. The cluster constraint
further depends on the normalization of the mass-temperature relation.
Therefore, combining the weak lensing and cluster abundance data can be used to
accurately calibrate the mass-temperature relation. We discuss this approach
and illustrate it using data from recent surveys.Comment: Matches the version in ApJL. Equation 4 corrected. Improvements in
the analysis move the cluster contours in Fig1 slightly upwards. No changes
in the conclusion
Plant-level Productivity and Imputation of Missing Data in U.S. Census Manufacturing Data
Within-industry differences in measured plant-level productivity are large. A large literature has been devoted to explaining the causes and consequences of these differences. In the U.S. Census Bureau's manufacturing data, the Bureau imputes for missing values using methods known to result in underestimation of variability and potential bias in multivariate inferences. We present an alternative strategy for handling the missing data based on multiple imputation via sequences of classification and regression trees. We use our imputations and the Bureau's imputations to estimate within-industry productivity dispersions. The results suggest that there is more within-industry productivity dispersion than previous research has indicated. We also estimate relationships between productivity and market structure and between output prices, capital, and the probability of plant exit (controlling for productivity) based on the improved imputations. For some estimands, we find substantially different results than those based on the Census Bureau's imputations.
Cosmological Implications of the Fundamental Relations of X-ray Clusters
Based on the two-parameter family nature of X-ray clusters of galaxies
obtained in a separate paper, we discuss the formation history of clusters and
cosmological parameters of the universe. Utilizing the spherical collapse model
of cluster formation, and assuming that the cluster X-ray core radius is
proportional to the virial radius at the time of the cluster collapse, the
observed relations among the density, radius, and temperature of clusters imply
that cluster formation occurs in a wide range of redshift. The observed
relations favor the low-density universe. Moreover, we find that the model of
is preferable.Comment: 7 pages, 4 figures. To be published in ApJ Letter
Cold dark matter models with high baryon content
Recent results have suggested that the density of baryons in the Universe,
OmegaB, is much more uncertain than previously thought, and may be
significantly higher. We demonstrate that a higher OmegaB increases the
viability of critical-density cold dark matter (CDM) models. High baryon
fraction offers the twin benefits of boosting the first peak in the microwave
anisotropy power spectrum and of suppressing short-scale power in the matter
power spectrum. These enable viable CDM models to have a larger Hubble constant
than otherwise possible. We carry out a general exploration of high OmegaB CDM
models, varying the Hubble constant h and the spectral index n. We confront a
variety of observational constraints and discuss specific predictions. Although
some observational evidence may favour baryon fractions as high as 20 per cent,
we find that values around 10 to 15 per cent provide a reasonable fit to a wide
range of data. We suggest that models with OmegaB in this range, with h about
0.5 and n about 0.8, are currently the best critical-density CDM models.Comment: 14 pages, LaTeX, with 9 included figures, to appear in MNRAS. Revised
version includes updated references, some changes to section 4. Conclusions
unchange
Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model
The cluster size dependence of superconductivity in the conventional
two-dimensional Hubbard model, commonly believed to describe high-temperature
superconductors, is systematically studied using the Dynamical Cluster
Approximation and Quantum Monte Carlo simulations as cluster solver. Due to the
non-locality of the d-wave superconducting order parameter, the results on
small clusters show large size and geometry effects. In large enough clusters,
the results are independent of the cluster size and display a finite
temperature instability to d-wave superconductivity.Comment: 4 pages, 3 figures; updated with version published in PRL; added
values of Tc obtained from fit
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