1,036 research outputs found
Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties
The wavelet transform, a family of orthonormal bases, is introduced as a
technique for performing multiresolution analysis in statistical mechanics. The
wavelet transform is a hierarchical technique designed to separate data sets
into sets representing local averages and local differences. Although
one-to-one transformations of data sets are possible, the advantage of the
wavelet transform is as an approximation scheme for the efficient calculation
of thermodynamic and ensemble properties. Even under the most drastic of
approximations, the resulting errors in the values obtained for average
absolute magnetization, free energy, and heat capacity are on the order of 10%,
with a corresponding computational efficiency gain of two orders of magnitude
for a system such as a Ising lattice. In addition, the errors in
the results tend toward zero in the neighborhood of fixed points, as determined
by renormalization group theory.Comment: 13 pages plus 7 figures (PNG
Entanglement renormalization and gauge symmetry
A lattice gauge theory is described by a redundantly large vector space that
is subject to local constraints, and can be regarded as the low energy limit of
an extended lattice model with a local symmetry. We propose a numerical
coarse-graining scheme to produce low energy, effective descriptions of lattice
models with a local symmetry, such that the local symmetry is exactly preserved
during coarse-graining. Our approach results in a variational ansatz for the
ground state(s) and low energy excitations of such models and, by extension, of
lattice gauge theories. This ansatz incorporates the local symmetry in its
structure, and exploits it to obtain a significant reduction of computational
costs. We test the approach in the context of the toric code with a magnetic
field, equivalent to Z2 lattice gauge theory, for lattices with up to 16 x 16
sites (16^2 x 2 = 512 spins) on a torus. We reproduce the well-known ground
state phase diagram of the model, consisting of a deconfined and spin polarized
phases separated by a continuous quantum phase transition, and obtain accurate
estimates of energy gaps, ground state fidelities, Wilson loops, and several
other quantities.Comment: reviewed version as published in PRB; this version includes a new
section about the accuracy of the results several corrections and added
citation
VTOL in ground effect flows for closely spaced jets
Results of a series of in ground effect twin jet tests are presented along with flow models for closely spaced jets to help predict pressure and upwash forces on simulated aircraft surfaces. The isolated twin jet tests revealed unstable fountains over a range of spacings and jet heights, regions of below ambient pressure on the ground, and negative pressure differential in the upwash flow field. A separate computer code was developed for vertically oriented, incompressible jets. This model more accurately reflects fountain behavior without fully formed wall jets, and adequately predicts ground isobars, upwash dynamic pressure decay, and fountain lift force variation with height above ground
Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models
Hierarchical lattices that constitute spatially anisotropic systems are
introduced. These lattices provide exact solutions for hierarchical models and,
simultaneously, approximate solutions for uniaxially or fully anisotropic d=3
physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers,
are obtained for Ising, XY magnetic models and percolation systems, including
crossovers from algebraic order to true long-range order.Comment: 7 pages, 12 figures. Corrected typos, added publication informatio
Possibility of s-wave pion condensates in neutron stars revisited
We examine possibilities of pion condensation with zero momentum (s-wave
condensation) in neutron stars by using the pion-nucleus optical potential U
and the relativistic mean field (RMF) models. We use low-density
phenomenological optical potentials parameterized to fit deeply bound pionic
atoms or pion-nucleus elastic scatterings. Proton fraction (Y_p) and electron
chemical potential (mu_e) in neutron star matter are evaluated in RMF models.
We find that the s-wave pion condensation hardly takes place in neutron stars
and especially has no chance if hyperons appear in neutron star matter and/or
b_1 parameter in U has density dependence.Comment: 4 pages, 3 figures, REVTe
Surface-peaked effective mass in the nuclear energy density functional and its influence on single-particle spectra
Calculations for infinite nuclear matter with realistic nucleon-nucleon
interactions suggest that the isoscalar effective mass of a nucleon at the
saturation density, m*/m, equals 0.8 +/- 0.1. This result is at variance with
empirical data on the level density in finite nuclei, which are consistent with
m*/m ~ 1. Ma and Wambach suggested that these two contradicting results may be
reconciled within a single theoretical framework by assuming a radial-dependent
effective mass, peaked at the nuclear surface. The aim of this exploratory work
is to investigate this idea within the density functional theory by using a
Skyrme-type local functional enriched with new terms, and , where and
denote the kinetic and particle densities, respectively. We show that each of
these terms can give rise to a surface peak in the effective mass, but of a
limited height. We investigate the influence of the radial profile of the
effective mass on the spin-orbit splittings and centroids. In particular, we
demonstrate that the term quenches the 1f5/2-1f7/2
splitting in 40Ca, which is strongly overestimated within conventional Skyrme
parametrizations.Comment: 8 pages, 8 figures, submitted to Phys. Rev.
The Ferromagnetic Potts model under an external magnetic field: an exact renormalization group approach
The q-state ferromagnetic Potts model under a non-zero magnetic field coupled
with the 0^th Potts state was investigated by an exact real-space
renormalization group approach. The model was defined on a family of diamond
hierarchical lattices of several fractal dimensions d_F. On these lattices, the
renormalization group transformations became exact for such a model when a
correlation coupling that singles out the 0^th Potts state was included in the
Hamiltonian. The rich criticality presented by the model with q=3 and d_F=2 was
fully analyzed. Apart from the Potts criticality for the zero field, an
Ising-like phase transition was found whenever the system was submitted to a
strong reverse magnetic field. Unusual characteristics such as cusps and
dimensional reduction were observed on the critical surface.Comment: 8 pages, 6 figures. Accepted to be published in Phys. Rev B (2006
Renormalization Group Approach to Strong-Coupled Superconductors
We develop an asymptotically exact renormalization group (RG) approach that
treats electron-electron and electron-phonon interactions on equal footing. The
approach allows an unbiased study of the instabilities of Fermi liquids without
the assumption of a broken symmetry. We apply our method to the problem of
strongly coupled superconductors and find the temperature T* below which the
high-temperature Fermi liquid state becomes unstable towards Cooper pairing. We
show that T* is the same as the critical temperature Tc obtained in
Eliashberg's strong coupling theory starting from the low-temperature
superconducting phase. We also show that Migdal's theorem is implicit in our
approach. Finally, our results lead to a novel way to calculate numerically,
from microscopic parameters, the transition temperature of superconductors.Comment: 6 pages, 3 figures, expanded presentation, final versio
Atomic excitations during the nuclear {\ss}- decay in light atoms
Probabilities of various final states are determined numerically for a number
of {\ss}- decaying light atoms. In our evaluations of the final state
probabilities we have used the highly accurate atomic wave functions
constructed for each few-electron atom/ion. We also discuss an experimental
possibility to observe negatively charged ions which form during the nuclear
{\ss}+ decays. High order corrections to the results obtained for {\ss}+/-
decays in few-electron atoms with the use of sudden approximation are
considered.Comment: 26 pages, 40 references, 6 tables and 0 figure
Magnetic models on Apollonian networks
Thermodynamic and magnetic properties of Ising models defined on the
triangular Apollonian network are investigated. This and other similar networks
are inspired by the problem of covering an Euclidian domain with circles of
maximal radii. Maps for the thermodynamic functions in two subsequent
generations of the construction of the network are obtained by formulating the
problem in terms of transfer matrices. Numerical iteration of this set of maps
leads to exact values for the thermodynamic properties of the model. Different
choices for the coupling constants between only nearest neighbors along the
lattice are taken into account. For both ferromagnetic and anti-ferromagnetic
constants, long range magnetic ordering is obtained. With exception of a size
dependent effective critical behavior of the correlation length, no evidence of
asymptotic criticality was detected.Comment: 21 pages, 5 figure
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