830 research outputs found
A Link Between the Semi-Major Axis of Extrasolar Gas Giant Planets and Stellar Metallicity
The fact that most extrasolar planets found to date are orbiting metal-rich
stars lends credence to the core accretion mechanism of gas giant planet
formation over its competitor, the disc instability mechanism. However, the
core accretion mechanism is not refined to the point of explaining orbital
parameters such as their unexpected semi-major axes and eccentricities. We
propose a model, which correlates the metallicity of the host star with the
original semi-major axis of its most massive planet, prior to migration,
considering that the core accretion scenario governs giant gas planet
formation. The model predicts that the optimum regions for planetary formation
shift inward as stellar metallicity decreases, providing an explanation for the
observed absence of long period planets in metal-poor stars. We compare our
predictions with the available data on extrasolar planets for stars with masses
similar to the mass of the Sun. A fitting procedure produces an estimate of
what we define as the Zero Age Planetary Orbit (ZAPO) curve as a function of
the metallicity of the star. The model also hints that the lack of planets
circling metal-poor stars may be partly caused by an enhanced destruction
probability during the migration process, since the planets lie initially
closer to the central stars.Comment: Nature of the replacement: According to recent simulations, the
temperature profile, T, is more adequately reproduced by beta = 1 rather than
beta = 2. We have introduced a distance scale factor that solves the very
fast drop of T for low metallicity and introduces naturally the inferior
distance limit of our ZAPO. Under this modification all the fitting process
was altere
Critical wave-packet dynamics in the power-law bond disordered Anderson Model
We investigate the wave-packet dynamics of the power-law bond disordered
one-dimensional Anderson model with hopping amplitudes decreasing as
. We consider the critical case ().
Using an exact diagonalization scheme on finite chains, we compute the
participation moments of all stationary energy eigenstates as well as the
spreading of an initially localized wave-packet. The eigenstates
multifractality is characterized by the set of fractal dimensions of the
participation moments. The wave-packet shows a diffusive-like spread developing
a power-law tail and achieves a stationary non-uniform profile after reflecting
at the chain boundaries. As a consequence, the time-dependent participation
moments exhibit two distinct scaling regimes. We formulate a finite-size
scaling hypothesis for the participation moments relating their scaling
exponents to the ones governing the return probability and wave-function
power-law decays
Delocalization and wave-packet dynamics in one-dimensional diluted Anderson models
We study the nature of one-electron eigen-states in a one-dimensional diluted
Anderson model where every Anderson impurity is diluted by a periodic function
. Using renormalization group and transfer matrix techniques, we provide
accurate estimates of the extended states which appear in this model, whose
number depends on the symmetry of the diluting function . The density of
states (DOS) for this model is also numerically obtained and its main features
are related to the symmetries of the diluting function . Further, we show
that the emergence of extended states promotes a sub-diffusive spread of an
initially localized wave-packet.Comment: 6 pages, 6 figures, to appear in EPJ
Bloch oscillations in an aperiodic one-dimensional potential
We study the dynamics of an electron subjected to a static uniform electric
field within a one-dimensional tight-binding model with a slowly varying
aperiodic potential. The unbiased model is known to support phases of localized
and extended one-electron states separated by two mobility edges. We show that
the electric field promotes sustained Bloch oscillations of an initial Gaussian
wave packet whose amplitude reflects the band width of extended states. The
frequency of these oscillations exhibit unique features, such as a sensitivity
to the initial wave packet position and a multimode structure for weak fields,
originating from the characteristics of the underlying aperiodic potential.Comment: 6 pages, 7 figure
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