2,291 research outputs found
Revisiting the effect of external fields in Axelrod's model of social dynamics
The study of the effects of spatially uniform fields on the steady-state
properties of Axelrod's model has yielded plenty of controversial results. Here
we re-examine the impact of this type of field for a selection of parameters
such that the field-free steady state of the model is heterogeneous or
multicultural. Analyses of both one and two-dimensional versions of Axelrod's
model indicate that, contrary to previous claims in the literature, the steady
state remains heterogeneous regardless of the value of the field strength.
Turning on the field leads to a discontinuous decrease on the number of
cultural domains, which we argue is due to the instability of zero-field
heterogeneous absorbing configurations. We find, however, that spatially
nonuniform fields that implement a consensus rule among the neighborhood of the
agents enforces homogenization. Although the overall effects of the fields are
essentially the same irrespective of the dimensionality of the model, we argue
that the dimensionality has a significant impact on the stability of the
field-free homogeneous steady state
Optical doping and damage formation in AIN by Eu implantation
AlN films grown on sapphire were implanted with 300 keV Eu ions to fluences from 3Ă1014 to 1.4Ă1017âatoms/cm2 in two different geometries: âchanneledâ along the c-axis and ârandomâ with a 10° angle between the ion beam and the surface normal. A detailed study of implantation damage accumulation is presented. Strong ion channeling effects are observed leading to significantly decreased damage levels for the channeled implantation within the entire fluence range. For random implantation, a buried amorphous layer is formed at the highest fluences. Red Eu-related photoluminescence at room temperature is observed in all samples with highest intensities for low damage samples (low fluence and channeled implantation) after annealing. Implantation damage, once formed, is shown to be stable up to very high temperatures.FCT - POCI/FIS/57550/2004FCT - PTDC/FIS/66262/2006FCT - PTDC/CTM/100756/200
Effect of Holstein phonons on the electronic properties of graphene
We obtain the self-energy of the electronic propagator due to the presence of
Holstein polarons within the first Born approximation. This leads to a
renormalization of the Fermi velocity of one percent. We further compute the
optical conductivity of the system at the Dirac point and at finite doping
within the Kubo-formula. We argue that the effects due to Holstein phonons are
negligible and that the Boltzmann approach which does not include inter-band
transition and can thus not treat optical phonons due to their high energy of
eV, remains valid.Comment: 13 pages, 4 figure
Wigner's little group and Berry's phase for massless particles
The ``little group'' for massless particles (namely, the Lorentz
transformations that leave a null vector invariant) is isomorphic to
the Euclidean group E2: translations and rotations in a plane. We show how to
obtain explicitly the rotation angle of E2 as a function of and we
relate that angle to Berry's topological phase. Some particles admit both signs
of helicity, and it is then possible to define a reduced density matrix for
their polarization. However, that density matrix is physically meaningless,
because it has no transformation law under the Lorentz group, even under
ordinary rotations.Comment: 4 pages revte
Generalized Entanglement as a Natural Framework for Exploring Quantum Chaos
We demonstrate that generalized entanglement [Barnum {\em et al.}, Phys. Rev.
A {\bf 68}, 032308 (2003)] provides a natural and reliable indicator of quantum
chaotic behavior. Since generalized entanglement depends directly on a choice
of preferred observables, exploring how generalized entanglement increases
under dynamical evolution is possible without invoking an auxiliary coupled
system or decomposing the system into arbitrary subsystems. We find that, in
the chaotic regime, the long-time saturation value of generalized entanglement
agrees with random matrix theory predictions. For our system, we provide
physical intuition into generalized entanglement within a single system by
invoking the notion of extent of a state. The latter, in turn, is related to
other signatures of quantum chaos.Comment: clarified and expanded version accepted by Europhys. Let
Stability of quantum motion and correlation decay
We derive a simple and general relation between the fidelity of quantum
motion, characterizing the stability of quantum dynamics with respect to
arbitrary static perturbation of the unitary evolution propagator, and the
integrated time auto-correlation function of the generator of perturbation.
Surprisingly, this relation predicts the slower decay of fidelity the faster
decay of correlations is. In particular, for non-ergodic and non-mixing
dynamics, where asymptotic decay of correlations is absent, a qualitatively
different and faster decay of fidelity is predicted on a time scale 1/delta as
opposed to mixing dynamics where the fidelity is found to decay exponentially
on a time-scale 1/delta^2, where delta is a strength of perturbation. A
detailed discussion of a semi-classical regime of small effective values of
Planck constant is given where classical correlation functions can be used to
predict quantum fidelity decay. Note that the correct and intuitively expected
classical stability behavior is recovered in the classical limit hbar->0, as
the two limits delta->0 and hbar->0 do not commute. In addition we also discuss
non-trivial dependence on the number of degrees of freedom. All the theoretical
results are clearly demonstrated numerically on a celebrated example of a
quantized kicked top.Comment: 32 pages, 10 EPS figures and 2 color PS figures. Higher resolution
color figures can be obtained from authors; minor changes, to appear in
J.Phys.A (March 2002
Statistics of opinion domains of the majority-vote model on a square lattice
The existence of juxtaposed regions of distinct cultures in spite of the fact
that people's beliefs have a tendency to become more similar to each other's as
the individuals interact repeatedly is a puzzling phenomenon in the social
sciences. Here we study an extreme version of the frequency-dependent bias
model of social influence in which an individual adopts the opinion shared by
the majority of the members of its extended neighborhood, which includes the
individual itself. This is a variant of the majority-vote model in which the
individual retains its opinion in case there is a tie among the neighbors'
opinions. We assume that the individuals are fixed in the sites of a square
lattice of linear size and that they interact with their nearest neighbors
only.
Within a mean-field framework, we derive the equations of motion for the
density of individuals adopting a particular opinion in the single-site and
pair approximations. Although the single-site approximation predicts a single
opinion domain that takes over the entire lattice, the pair approximation
yields a qualitatively correct picture with the coexistence of different
opinion domains and a strong dependence on the initial conditions. Extensive
Monte Carlo simulations indicate the existence of a rich distribution of
opinion domains or clusters, the number of which grows with whereas the
size of the largest cluster grows with . The analysis of the sizes of
the opinion domains shows that they obey a power-law distribution for not too
large sizes but that they are exponentially distributed in the limit of very
large clusters. In addition, similarly to other well-known social influence
model -- Axelrod's model -- we found that these opinion domains are unstable to
the effect of a thermal-like noise
Lorentz transformations that entangle spins and entangle momenta
Simple examples are presented of Lorentz transformations that entangle the
spins and momenta of two particles with positive mass and spin 1/2. They apply
to indistinguishable particles, produce maximal entanglement from finite
Lorentz transformations of states for finite momenta, and describe entanglement
of spins produced together with entanglement of momenta. From the entanglements
considered, no sum of entanglements is found to be unchanged.Comment: 5 Pages, 2 Figures, One new paragraph and reference adde
On the "Mandelbrot set" for a pair of linear maps and complex Bernoulli convolutions
We consider the "Mandelbrot set" for pairs of complex linear maps,
introduced by Barnsley and Harrington in 1985 and studied by Bousch, Bandt and
others. It is defined as the set of parameters in the unit disk such
that the attractor of the IFS is
connected. We show that a non-trivial portion of near the imaginary axis is
contained in the closure of its interior (it is conjectured that all non-real
points of are in the closure of the set of interior points of ). Next we
turn to the attractors themselves and to natural measures
supported on them. These measures are the complex analogs of
much-studied infinite Bernoulli convolutions. Extending the results of Erd\"os
and Garsia, we demonstrate how certain classes of complex algebraic integers
give rise to singular and absolutely continuous measures . Next we
investigate the Hausdorff dimension and measure of , for
in the set , for Lebesgue-a.e. . We also obtain partial results on
the absolute continuity of for a.e. of modulus greater
than .Comment: 22 pages, 5 figure
Electronic transport in graphene: A semi-classical approach including midgap states
Using the semi-classical Boltzmann theory, we calculate the conductivity as
function of the carrier density. As usually, we include the scattering from
charged impurities, but conclude that the estimated impurity density is too low
in order to explain the experimentally observed mobilities. We thus propose an
additional scattering mechanism involving midgap states which leads to a
similar k-dependence of the relaxation time as charged impurities. The new
scattering mechanism can account for the experimental findings such as the
sublinear behavior of the conductivity versus gate voltage and the increase of
the minimal conductivity for clean samples. We also discuss temperature
dependent scattering due to acoustic phonons.Comment: 10 pages, 4 figure
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