6,953 research outputs found
Effects of Helium Phase Separation on the Evolution of Extrasolar Giant Planets
We build on recent new evolutionary models of Jupiter and Saturn and here
extend our calculations to investigate the evolution of extrasolar giant
planets of mass 0.15 to 3.0 M_J. Our inhomogeneous thermal history models show
that the possible phase separation of helium from liquid metallic hydrogen in
the deep interiors of these planets can lead to luminosities ~2 times greater
than have been predicted by homogeneous models. For our chosen phase diagram
this phase separation will begin to affect the planets' evolution at ~700 Myr
for a 0.15 M_J object and ~10 Gyr for a 3.0 M_J object. We show how phase
separation affects the luminosity, effective temperature, radii, and
atmospheric helium mass fraction as a function of age for planets of various
masses, with and without heavy element cores, and with and without the effect
of modest stellar irradiation. This phase separation process will likely not
affect giant planets within a few AU of their parent star, as these planets
will cool to their equilibrium temperatures, determined by stellar heating,
before the onset of phase separation. We discuss the detectability of these
objects and the likelihood that the energy provided by helium phase separation
can change the timescales for formation and settling of ammonia clouds by
several Gyr. We discuss how correctly incorporating stellar irradiation into
giant planet atmosphere and albedo modeling may lead to a consistent
evolutionary history for Jupiter and Saturn.Comment: 22 pages, including 14 figures. Accepted to the Astrophysical Journa
Compressibility of the Two-Dimensional infinite-U Hubbard Model
We study the interactions between the coherent quasiparticles and the
incoherent Mott-Hubbard excitations and their effects on the low energy
properties in the Hubbard model. Within the framework of a
systematic large-N expansion, these effects first occur in the next to leading
order in 1/N. We calculate the scattering phase shift and the free energy, and
determine the quasiparticle weight Z, mass renormalization, and the
compressibility. It is found that the compressibility is strongly renormalized
and diverges at a critical doping . We discuss the nature
of this zero-temperature phase transition and its connection to phase
separation and superconductivity.Comment: 4 pages, 3 eps figures, final version to appear in Phys. Rev. Let
Cumulant expansion of the periodic Anderson model in infinite dimension
The diagrammatic cumulant expansion for the periodic Anderson model with
infinite Coulomb repulsion () is considered here for an hypercubic
lattice of infinite dimension (). The same type of simplifications
obtained by Metzner for the cumulant expansion of the Hubbard model in the
limit of , are shown to be also valid for the periodic Anderson
model.Comment: 13 pages, 7 figures.ps. To be published in J. Phys. A: Mathematical
and General (1997
Breadboard stellar tracker system test report, volume 1
The performance of a star tracker equipped with a focal plane detector was evaluated. The CID board is an array of 256 x 256 pixels which are 20 x 20 micrometers in dimension. The tracker used for test was a breadboard tracker system developed by BASD. Unique acquisition and tracking algorithms are employed to enhance performance. A pattern recognition process is used to test for proper image spread function and to avoid false acquisition on noise. A very linear, high gain, interpixel transfer function is derived for interpolating star position. The lens used in the tracker has an EFL of 100 mm. The tracker has an FOV of 2.93 degrees resulting in a pixel angular subtense of 41.253 arc sec in each axis. The test procedure used for the program presented a star to the tracker in a circular pattern of positions; the pattern was formed by projecting a simulated star through a rotatable deviation wedge. Further tests determined readout noise, Noise Equivalent Displacement during track, and spatial noise during acquisition by taking related data and reducing it
Strong-Coupling Expansion for the Hubbard Model
A strong-coupling expansion for models of correlated electrons in any
dimension is presented. The method is applied to the Hubbard model in
dimensions and compared with numerical results in . Third order expansion
of the Green function suffices to exhibit both the Mott metal-insulator
transition and a low-temperature regime where antiferromagnetic correlations
are strong. It is predicted that some of the weak photoemission signals
observed in one-dimensional systems such as should become stronger as
temperature increases away from the spin-charge separated state.Comment: 4 pages, RevTex, 3 epsf figures include
Ferromagnetism in the Periodic Anderson Model - a Modified Alloy Analogy
We introduce a new aproximation scheme for the periodic Anderson model (PAM).
The modified alloy approximation represents an optimum alloy approximation for
the strong coupling limit, which can be solved within the CPA-formalism.
Zero-temperature and finite-temperature phase diagrams are presented for the
PAM in the intermediate-valence regime. The diversity of magnetic properties
accessible by variation of the system parameters can be studied by means of
quasiparticle densities of states: The conduction band couples either ferro- or
antiferromagneticaly to the f-levels. A finite hybridization is a necessary
precondition for ferromagnetism. However, too strong hybridization generally
suppresses ferromagnetism, but can for certain system parameters also lead to a
semi-metallic state with unusual magnetic properties. By comparing with the
spectral density approximation, the influence of quasiparticle damping can be
examined.Comment: 20 pages, 13 figure
Variational Cluster Perturbation Theory for Bose-Hubbard models
We discuss the application of the variational cluster perturbation theory
(VCPT) to the Mott-insulator--to--superfluid transition in the Bose-Hubbard
model. We show how the VCPT can be formulated in such a way that it gives a
translation invariant excitation spectrum -- free of spurious gaps -- despite
the fact that if formally breaks translation invariance. The phase diagram and
the single-particle Green function in the insulating phase are obtained for
one-dimensional systems. When the chemical potential of the cluster is taken as
a variational parameter, the VCPT reproduces the dimension dependence of the
phase diagram even for one-site clusters. We find a good quantitative agreement
with the results of the density-matrix renormalization group when the number of
sites in the cluster becomes of order 10. The extension of the method to the
superfluid phase is discussed.Comment: v1) 10 pages, 6 figures. v2) Final version as publishe
Metal-Insulator Transition in the Two-Dimensional Hubbard Model at Half-Filling with Lifetime Effects within the Moment Approach
We explore the effect of the imaginary part of the self-energy,
, having a single pole, ,
with spectral weight, , and quasi-particle lifetime,
, on the density of states. We solve the set of parameters,
), , and by means of
the moment approach (exact sum rules) of Nolting. Our choice for
, satisfies the Kramers - Kronig relationship automatically.
Due to our choice of the self - energy, the system is not a Fermi liquid for
any value of the interaction, a result which is also true in the moment
approach of Nolting without lifetime effects. By increasing the value of the
local interaction, , at half-filling (), we go from a
paramagnetic metal to a paramagnetic insulator, (Mott metal - insulator
transition ()) for values of of the order of ( is
the band width) which is in agreement with numerical results for finite
lattices and for infinity dimensions (). These results settle down
the main weakness of the spherical approximation of Nolting: a finite gap for
any finite value of the interaction, i.e., an insulator for any finite value of
. Lifetime effects are absolutely indispensable. Our scheme works better
than the one of improving the narrowing band factor, , beyond the
spherical approximation of Nolting.Comment: 5 pages and 5 ps figures (included
Planetary Radii across Five Orders of Magnitude in Mass and Stellar Insolation: Application to Transits
To aid in the physical interpretation of planetary radii constrained through
observations of transiting planets, or eventually direct detections, we compute
model radii of pure hydrogen-helium, water, rock, and iron planets, along with
various mixtures. Masses ranging from 0.01 Earth masses to 10 Jupiter masses at
orbital distances of 0.02 to 10 AU are considered. For hydrogen-helium rich
planets, our models are the first to couple planetary evolution to stellar
irradiation over a wide range of orbital separations (0.02 to 10 AU) through a
non-gray radiative-convective equilibrium atmosphere model. Stellar irradiation
retards the contraction of giant planets, but its effect is not a simple
function of the irradiation level: a planet at 1 AU contracts as slowly as a
planet at 0.1 AU. For hydrogen-helium planets, we consider cores up to 90% of
the total planet mass, comparable to those of Uranus and Neptune. If "hot
Neptunes" have maintained their original masses and are not remnants of more
massive planets, radii of 0.30-0.45 times Jupiter's radius are expected. Water
planets are ~40-50% larger than rocky planets, independent of mass. Finally, we
provide tables of planetary radii at various ages and compositions, and for
ice-rock-iron planets we fit our results to analytic functions, which will
allow for quick composition estimates, given masses and radii, or mass
estimates, given only planetary radii. These results will assist in the
interpretation of observations for both the current transiting planet surveys
as well as upcoming space missions, including CoRoT and Kepler.Comment: Published in The Astrophysical Journal 2007 April. This revision
corrects coefficient errors in equations 7 and 8. Erratum sent to Ap
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