6,555 research outputs found
Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction
Replacing linear diffusion by a degenerate diffusion of porous medium type is
known to regularize the classical two-dimensional parabolic-elliptic
Keller-Segel model. The implications of nonlinear diffusion are that solutions
exist globally and are uniformly bounded in time. We analyse the stationary
case showing the existence of a unique, up to translation, global minimizer of
the associated free energy. Furthermore, we prove that this global minimizer is
a radially decreasing compactly supported continuous density function which is
smooth inside its support, and it is characterized as the unique compactly
supported stationary state of the evolution model. This unique profile is the
clear candidate to describe the long time asymptotics of the diffusion
dominated classical Keller-Segel model for general initial data.Comment: 30 pages, 2 figure
Patchy He II reionization and the physical state of the IGM
We present a Monte-Carlo model of He II reionization by QSOs and its effect
on the thermal state of the clumpy intergalactic medium (IGM). The model
assumes that patchy reionization develops as a result of the discrete
distribution of QSOs. It includes various recipes for the propagation of the
ionizing photons, and treats photo-heating self-consistently. The model
provides the fraction of He III, the mean temperature in the IGM, and the He II
mean optical depth -- all as a function of redshift. It also predicts the
evolution of the local temperature versus density relation during reionization.
Our findings are as follows: The fraction of He III increases gradually until
it becomes close to unity at . The He II mean optical depth
decreases from at to at .
The mean temperature rises gradually between and and
declines slowly at lower redshifts. The model predicts a flattening of the
temperature-density relation with significant increase in the scatter during
reionization at . Towards the end of reionization the scatter is
reduced and a tight relation is re-established. This scatter should be
incorporated in the analysis of the Ly forest at . Comparison
with observational results of the optical depth and the mean temperature at
moderate redshifts constrains several key physical parameters.Comment: 18 pages, 9 figures; Changed content. Accepted for publication in
MNRA
{\delta}N formalism
Precise understanding of nonlinear evolution of cosmological perturbations
during inflation is necessary for the correct interpretation of measurements of
non-Gaussian correlations in the cosmic microwave background and the
large-scale structure of the universe. The "{\delta}N formalism" is a popular
and powerful technique for computing non-linear evolution of cosmological
perturbations on large scales. In particular, it enables us to compute the
curvature perturbation, {\zeta}, on large scales without actually solving
perturbed field equations. However, people often wonder why this is the case.
In order for this approach to be valid, the perturbed Hamiltonian constraint
and matter-field equations on large scales must, with a suitable choice of
coordinates, take on the same forms as the corresponding unperturbed equations.
We find that this is possible when (1) the unperturbed metric is given by a
homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker metric; and (2)
on large scales and with a suitable choice of coordinates, one can ignore the
shift vector (g0i) as well as time-dependence of tensor perturbations to
gij/a2(t) of the perturbed metric. While the first condition has to be assumed
a priori, the second condition can be met when (3) the anisotropic stress
becomes negligible on large scales. However, in order to explicitly show that
the second condition follows from the third condition, one has to use
gravitational field equations, and thus this statement may depend on the
details of theory of gravitation. Finally, as the {\delta}N formalism uses only
the Hamiltonian constraint and matter-field equations, it does not a priori
respect the momentum constraint. We show that the violation of the momentum
constraint only yields a decaying mode solution for {\zeta}, and the violation
vanishes when the slow-roll conditions are satisfied.Comment: 10 page
Quantum Monte Carlo method using phase-free random walks with Slater determinants
We develop a quantum Monte Carlo method for many fermions that allows the use
of any one-particle basis. It projects out the ground state by random walks in
the space of Slater determinants. An approximate approach is formulated to
control the phase problem with a trial wave function . Using
plane-wave basis and non-local pseudopotentials, we apply the method to Si
atom, dimer, and 2, 16, 54 atom (216 electrons) bulk supercells. Single Slater
determinant wave functions from density functional theory calculations were
used as with no additional optimization. The calculated binding
energy of Si2 and cohesive energy of bulk Si are in excellent agreement with
experiments and are comparable to the best existing theoretical results.Comment: 5 pages, Latex, with 1 fi
Pentaquark decay is suppressed by chirality conservation
It is shown, that if the pentaquark baryon can be
represented by the local quark current , its decay is forbidden in the limit of chirality conservation. The
decay width is proportional to , where , is quark condensate, and,
therefore, is strongly suppressed. Also the polarization operator of the
pentaquark current with isospin 1 is calculated using the operator product
expansion and estimation for it mass is obtained .Comment: 4 pages, 1 fig, typos correcte
Time-dependent density functional theory for strong electromagnetic fields in crystalline solids
We apply the coupled dynamics of time-dependent density functional theory and
Maxwell equations to the interaction of intense laser pulses with crystalline
silicon. As a function of electromagnetic field intensity, we see several
regions in the response. At the lowest intensities, the pulse is reflected and
transmitted in accord with the dielectric response, and the characteristics of
the energy deposition is consistent with two-photon absorption. The absorption
process begins to deviate from that at laser intensities ~ 10^13 W/cm^2, where
the energy deposited is of the order of 1 eV per atom. Changes in the
reflectivity are seen as a function of intensity. When it passes a threshold of
about 3 \times 1012 W/cm2, there is a small decrease. At higher intensities,
above 2 \times 10^13 W/cm^2, the reflectivity increases strongly. This behavior
can be understood qualitatively in a model treating the excited electron-hole
pairs as a plasma.Comment: 27 pages; 11 figure
Optical evidence for the proximity to a spin-density-wave metallic state in NaCoO
We present the optical properties of \na single crystals, measured over a
broad spectral range as a function of temperature (). The capability to
cover the energy range from the far-infrared up to the ultraviolet allows us to
perform reliable Kramers-Kronig transformation, in order to obtain the
absorption spectrum (i.e., the complex optical conductivity). To the complex
optical conductivity we apply the generalized Drude model, extracting the
frequency dependence of the scattering rate () and effective mass
() of the itinerant charge carriers. We find that at low temperatures and for . This suggests that \na is at
the verge of a spin-density-wave metallic phase
Projective Quantum Monte Carlo Method for the Anderson Impurity Model and its Application to Dynamical Mean Field Theory
We develop a projective quantum Monte Carlo algorithm of the Hirsch-Fye type
for obtaining ground state properties of the Anderson impurity model. This
method is employed to solve the self-consistency equations of dynamical mean
field theory. It is shown that the approach converges rapidly to the ground
state so that reliable zero-temperature results are obtained. As a first
application, we study the Mott-Hubbard metal-insulator transition of the
one-band Hubbard model, reconfirming the numerical renormalization group
results.Comment: 4 pages, 4 figure
Energy-level statistics and localization of 2d electrons in random magnetic fields
Using the method of energy-level statistics, the localization properties of
electrons moving in two dimensions in the presence of a perpendicular random
magnetic field and additional random disorder potentials are investigated. For
this model, extended states have recently been proposed to exist in the middle
of the band. In contrast, from our calculations of the large- behavior of
the nearest neighbor level spacing distribution and from a finite size
scaling analysis we find only localized states in the suggested energy and
disorder range.Comment: 4 pages LaTeX, 4 eps-figures. to appear in Physica
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