62,536 research outputs found
Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields
We present an exact algebraic solution of a single graphene plane in
transverse electric and perpendicular magnetic fields. The method presented
gives both the eigen-values and the eigen-functions of the graphene plane. It
is shown that the eigen-states of the problem can be casted in terms of
coherent states, which appears in a natural way from the formalism.Comment: 11 pages, 5 figures, accepted for publication in Journal of Physics
Condensed Matte
Cluster detection in networks using percolation
We consider the task of detecting a salient cluster in a sensor network, that
is, an undirected graph with a random variable attached to each node. Motivated
by recent research in environmental statistics and the drive to compete with
the reigning scan statistic, we explore alternatives based on the percolative
properties of the network. The first method is based on the size of the largest
connected component after removing the nodes in the network with a value below
a given threshold. The second method is the upper level set scan test
introduced by Patil and Taillie [Statist. Sci. 18 (2003) 457-465]. We establish
the performance of these methods in an asymptotic decision- theoretic framework
in which the network size increases. These tests have two advantages over the
more conventional scan statistic: they do not require previous information
about cluster shape, and they are computationally more feasible. We make
abundant use of percolation theory to derive our theoretical results, and
complement our theory with some numerical experiments.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ412 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Renormalization group and Ward identities in quantum liquid phases and in unconventional critical phenomena
By reviewing the application of the renormalization group to different
theoretical problems, we emphasize the role played by the general symmetry
properties in identifying the relevant running variables describing the
behavior of a given physical system. In particular, we show how the constraints
due to the Ward identities, which implement the conservation laws associated
with the various symmetries, help to minimize the number of independent running
variables. This use of the Ward identities is examined both in the case of a
stable phase and of a critical phenomenon. In the first case we consider the
problems of interacting fermions and bosons. In one dimension general and
specific Ward identities are sufficient to show the non-Fermi-liquid character
of the interacting fermion system, and also allow to describe the crossover to
a Fermi liquid above one dimension. This crossover is examined both in the
absence and presence of singular interaction. On the other hand, in the case of
interacting bosons in the superfluid phase, the implementation of the Ward
identities provides the asymptotically exact description of the acoustic
low-energy excitation spectrum, and clarifies the subtle mechanism of how this
is realized below and above three dimensions. As a critical phenomenon, we
discuss the disorder-driven metal-insulator transition in a disordered
interacting Fermi system. In this case, through the use of Ward identities, one
is able to associate all the disorder effects to renormalizations of the Landau
parameters. As a consequence, the occurrence of a metal-insulator transition is
described as a critical breakdown of a Fermi liquid.Comment: 47 pages, 11 figure
Scaling cosmology with variable dark-energy equation of state
Interactions between dark matter and dark energy which result in a power-law
behavior (with respect to the cosmic scale factor) of the ratio between the
energy densities of the dark components (thus generalizing the LCDM model) have
been considered as an attempt to alleviate the cosmic coincidence problem
phenomenologically. We generalize this approach by allowing for a variable
equation of state for the dark energy within the CPL-parametrization. Based on
analytic solutions for the Hubble rate and using the Constitution and Union2
SNIa sets, we present a statistical analysis and classify different interacting
and non-interacting models according to the Akaike (AIC) and the Bayesian (BIC)
information criteria. We do not find noticeable evidence for an alleviation of
the coincidence problem with the mentioned type of interaction.Comment: 21 pages, 11 figures, 11 tables, discussion improve
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