1,509 research outputs found
Magnetic and Dynamic Properties of the Hubbard Model in Infinite Dimensions
An essentially exact solution of the infinite dimensional Hubbard model is
made possible by using a self-consistent mapping of the Hubbard model in this
limit to an effective single impurity Anderson model. Solving the latter with
quantum Monte Carlo procedures enables us to obtain exact results for the one
and two-particle properties of the infinite dimensional Hubbard model. In
particular we find antiferromagnetism and a pseudogap in the single-particle
density of states for sufficiently large values of the intrasite Coulomb
interaction at half filling. Both the antiferromagnetic phase and the
insulating phase above the N\'eel temperature are found to be quickly
suppressed on doping. The latter is replaced by a heavy electron metal with a
quasiparticle mass strongly dependent on doping as soon as . At half
filling the antiferromagnetic phase boundary agrees surprisingly well in shape
and order of magnitude with results for the three dimensional Hubbard model.Comment: 32 page
Density Matrix Functional Calculations for Matter in Strong Magnetic Fields: I. Atomic Properties
We report on a numerical study of the density matrix functional introduced by
Lieb, Solovej and Yngvason for the investigation of heavy atoms in high
magnetic fields. This functional describes {\em exactly} the quantum mechanical
ground state of atoms and ions in the limit when the nuclear charge and the
electron number tend to infinity with fixed, and the magnetic field
tends to infinity in such a way that . We have
calculated electronic density profiles and ground state energies for values of
the parameters that prevail on neutron star surfaces and compared them with
results obtained by other methods. For iron at G the ground state
energy differs by less than 2 \% from the Hartree-Fock value. We have also
studied the maximal negative ionization of heavy atoms in this model at various
field strengths. In contrast to Thomas-Fermi type theories atoms can bind
excess negative charge in the density matrix model. For iron at G
the maximal excess charge in this model corresponds to about one electron.Comment: Revtex, 13 pages with 6 eps figures include
Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations
We investigate how the dynamics of a single chain influences the kinetics of
early stage phase separation in a symmetric binary polymer mixture. We consider
quenches from the disordered phase into the region of spinodal instability. On
a mean field level we approach this problem with two methods: a dynamical
extension of the self consistent field theory for Gaussian chains, with the
density variables evolving in time, and the method of the external potential
dynamics where the effective external fields are propagated in time. Different
wave vector dependencies of the kinetic coefficient are taken into account.
These early stages of spinodal decomposition are also studied through Monte
Carlo simulations employing the bond fluctuation model that maps the chains --
in our case with 64 effective segments -- on a coarse grained lattice. The
results obtained through self consistent field calculations and Monte Carlo
simulations can be compared because the time, length, and temperature scales
are mapped onto each other through the diffusion constant, the chain extension,
and the energy of mixing. The quantitative comparison of the relaxation rate of
the global structure factor shows that a kinetic coefficient according to the
Rouse model gives a much better agreement than a local, i.e. wave vector
independent, kinetic factor. Including fluctuations in the self consistent
field calculations leads to a shorter time span of spinodal behaviour and a
reduction of the relaxation rate for smaller wave vectors and prevents the
relaxation rate from becoming negative for larger values of the wave vector.
This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin
Thermodynamics of non-local materials: extra fluxes and internal powers
The most usual formulation of the Laws of Thermodynamics turns out to be
suitable for local or simple materials, while for non-local systems there are
two different ways: either modify this usual formulation by introducing
suitable extra fluxes or express the Laws of Thermodynamics in terms of
internal powers directly, as we propose in this paper. The first choice is
subject to the criticism that the vector fluxes must be introduced a posteriori
in order to obtain the compatibility with the Laws of Thermodynamics. On the
contrary, the formulation in terms of internal powers is more general, because
it is a priori defined on the basis of the constitutive equations. Besides it
allows to highlight, without ambiguity, the contribution of the internal powers
in the variation of the thermodynamic potentials. Finally, in this paper, we
consider some examples of non-local materials and derive the proper expressions
of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic
Crystal and magnetic structure of LaTiO3 : evidence for non-degenerate -orbitals
The crystal and magnetic structure of LaTiO3 ~ has been studied by x-ray and
neutron diffraction techniques using nearly stoichiometric samples. We find a
strong structural anomaly near the antiferromagnetic ordering, T=146 K. In
addition, the octahedra in LaTiO3 exhibit an intrinsic distortion which implies
a splitting of the t2g-levels. Our results indicate that LaTiO3 should be
considered as a Jahn-Teller system where the structural distortion and the
resulting level splitting are enhanced by the magnetic ordering.Comment: 4 pages 5 figure
Experimental properties of Bose-Einstein condensates in 1D optical lattices: Bloch oscillations, Landau-Zener tunneling and mean-field effects
We report experimental results on the properties of Bose-Einstein condensates
in 1D optical lattices. By accelerating the lattice, we observed Bloch
oscillations of the condensate in the lowest band, as well as Landau-Zener
(L-Z) tunneling into higher bands when the lattice depth was reduced and/or the
acceleration of the lattice was increased. The dependence of the L-Z tunneling
rate on the condensate density was then related to mean-field effects modifying
the effective potential acting on the condensate, yielding good agreement with
recent theoretical work. We also present several methods for measuring the
lattice depth and discuss the effects of the micromotion in the TOP-trap on our
experimental results.Comment: 11 pages, 14 figure
The Hubbard Model at Infinite Dimensions: Thermodynamic and Transport Properties
We present results on thermodynamic quantities, resistivity and optical
conductivity for the Hubbard model on a simple hypercubic lattice in infinite
dimensions. Our results for the paramagnetic phase display the features
expected from an intuitive analysis of the one-particle spectra and
substantiate the similarity of the physics of the Hubbard model to those of
heavy fermion systems. The calculations were performed using an approximate
solution to the single-impurity Anderson model, which is the key quantity
entering the solution of the Hubbard model in this limit. To establish the
quality of this approximation we compare its results, together with those
obtained from two other widely used methods, to essentially exact quantum Monte
Carlo results.Comment: 29 pages, 16 figure
The large longitudinal spread of solar energetic particles during the January 17, 2010 solar event
We investigate multi-spacecraft observations of the January 17, 2010 solar
energetic particle event. Energetic electrons and protons have been observed
over a remarkable large longitudinal range at the two STEREO spacecraft and
SOHO suggesting a longitudinal spread of nearly 360 degrees at 1AU. The flaring
active region, which was on the backside of the Sun as seen from Earth, was
separated by more than 100 degrees in longitude from the magnetic footpoints of
each of the three spacecraft. The event is characterized by strongly delayed
energetic particle onsets with respect to the flare and only small or no
anisotropies in the intensity measurements at all three locations. The presence
of a coronal shock is evidenced by the observation of a type II radio burst
from the Earth and STEREO B. In order to describe the observations in terms of
particle transport in the interplanetary medium, including perpendicular
diffusion, a 1D model describing the propagation along a magnetic field line
(model 1) (Dr\"oge, 2003) and the 3D propagation model (model 2) by (Dr\"oge et
al., 2010) including perpendicular diffusion in the interplanetary medium have
been applied, respectively. While both models are capable of reproducing the
observations, model 1 requires injection functions at the Sun of several hours.
Model 2, which includes lateral transport in the solar wind, reveals high
values for the ratio of perpendicular to parallel diffusion. Because we do not
find evidence for unusual long injection functions at the Sun we favor a
scenario with strong perpendicular transport in the interplanetary medium as
explanation for the observations.Comment: The final publication is available at http://www.springerlink.co
The Liquid-Gas Phase Transitions in a Multicomponent Nuclear System with Coulomb and Surface Effects
The liquid-gas phase transition is studied in a multi-component nuclear
system using a local Skyrme interaction with Coulomb and surface effects. Some
features are qualitatively the same as the results of Muller and Serot which
uses relativistic mean field without Coulomb and surface effects. Surface
tension brings the coexistance binodal surface to lower pressure. The Coulomb
interaction makes the binodal surface smaller and cause another pair of binodal
points at low pressure and large proton fraction with less protons in liquid
phase and more protons in gas phase.Comment: 20 pages including 7 postscript figure
Symmetric generation of Coxeter groups
We provide involutory symmetric generating sets of finitely generated Coxeter
groups, fulfilling a suitable finiteness condition, which in particular is
fulfilled in the finite, affine and compact hyperbolic cases.Comment: 11 pages, 11 figure
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