528,119 research outputs found
Localization of Matters on a String-like Defect
After presenting string-like solutions with a warp factor to Einstein's
equations, we study localization of various spin fields on a string-like defect
in a general space-time dimension from the viewpoint of field theory. It is
shown that spin 0 and 2 fields are localized on a defect with the exponentially
decreasing warp factor. Spin 1 field can be also localized on a defect with the
exponentially decreasing warp factor. On the other hand, spin one-half and
three-half fields can be localized on a defect with the exponentially
increasing warp factor, provided that additional interactions are not
introduced. Thus, some mechanism of localization must be invoked for these
fermionic fields. These results are very similar to those of a domain wall in
five space-time dimensions except the case of spin 1 field.Comment: 15 pages, LaTex 2e, minor corrections (to appear in Phys. Lett. B
The Defect of Random Hyperspherical Harmonics
Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the
unit -sphere (). We investigate the distribution of their defect
i.e., the difference between the measure of positive and negative regions.
Marinucci and Wigman studied the two-dimensional case giving the asymptotic
variance (Marinucci and Wigman 2011) and a Central Limit Theorem (Marinucci and
Wigman 2014), both in the high-energy limit. Our main results concern
asymptotics for the defect variance and quantitative CLTs in Wasserstein
distance, in any dimension. The proofs are based on Wiener-It\^o chaos
expansions for the defect, a careful use of asymptotic results for all order
moments of Gegenbauer polynomials and Stein-Malliavin approximation techniques
by Nourdin and Peccati. Our argument requires some novel technical results of
independent interest that involve integrals of the product of three
hyperspherical harmonics.Comment: Accepted for publication in Journal of Theoretical Probabilit
Defect CFTs and holographic multiverse
We investigate some aspects of a recent proposal for a holographic
description of the multiverse. Specifically, we focus on the implications on
the suggested duality of the fluctuations of a bubble separating two universes
with different cosmological constants. We do so by considering a similar
problem in a 2+1 CFT with a codimension one defect, obtained by an M5-brane
probe embedding in AdS_4x S^7, and studying its spectrum of fluctuations. Our
results suggest that the kind of behavior required by the spectrum of bubble
fluctuations is not likely to take place in defect CFTs with an AdS dual,
although it might be possible if the defect supports a non-unitary theory.Comment: 19 pages; v2: typos fixed, minor changes
Systematic Study of Electron Localization in an Amorphous Semiconductor
We investigate the electronic structure of gap and band tail states in
amorphous silicon. Starting with two 216-atom models of amorphous silicon with
defect concentration close to the experiments, we systematically study the
dependence of electron localization on basis set, density functional and spin
polarization using the first principles density functional code Siesta. We
briefly compare three different schemes for characterizing localization:
information entropy, inverse participation ratio and spatial variance. Our
results show that to accurately describe defect structures within self
consistent density functional theory, a rich basis set is necessary. Our study
revealed that the localization of the wave function associated with the defect
states decreases with larger basis sets and there is some enhancement of
localization from GGA relative to LDA. Spin localization results obtained via
LSDA calculations, are in reasonable agreement with experiment and with
previous LSDA calculations on a-Si:H models.Comment: 16 pages, 11 Postscript figures, To appear in Phys. Rev.
The Virtue of Defects in 4D Gauge Theories and 2D CFTs
We advance a correspondence between the topological defect operators in
Liouville and Toda conformal field theories - which we construct - and loop
operators and domain wall operators in four dimensional N=2 supersymmetric
gauge theories on S^4. Our computation of the correlation functions in
Liouville/Toda theory in the presence of topological defect operators, which
are supported on curves on the Riemann surface, yields the exact answer for the
partition function of four dimensional gauge theories in the presence of
various walls and loop operators; results which we can quantitatively
substantiate with an independent gauge theory analysis. As an interesting
outcome of this work for two dimensional conformal field theories, we prove
that topological defect operators and the Verlinde loop operators are different
descriptions of the same operators.Comment: 59 pages, latex; v2 corrections to some formula
On topological defect formation in the process of symmetry breaking phase transitions
By resorting to some results in quantum field theories with spontaneous
breakdown of symmetry we show that an explanation based on microscopic dynamics
can be given of the fact that topological defect formation is observed during
the process of non-equilibrium phase transitions characterized by a non-zero
order parameter. We show that the Nambu-Goldstone particle acquires an
effective non-zero mass due to the boundary (finite volume) effects and this is
related with the size of the defect. We also relate such volume effect with
temperature effect.Comment: 12 pages, no figure
Local polariton modes and resonant tunneling of electromagnetic waves through periodic Bragg multiple quantum well structures
We study analytically defect polariton states in Bragg multiple-quantum-well
structures and defect induced changes in transmission and reflection spectra.
Defect layers can differ from the host layers in three ways: exciton-light
coupling strength, exciton resonance frequency, and inter-well spacing. We show
that a single defect leads to two local polariton modes in the photonic
bandgap. These modes cause peculiarities in reflection and transmission
spectra. Each type of defect can be reproduced experimentally, and we show that
each of these plays a distinct role in the optical properties of the system.
For some defects, we predict a narrow transmission window in the forbidden gap
at the frequency set by parameters of the defect. We obtain analytical
expressions for corresponding local frequencies as well as for reflection and
transmission coefficients. We show that the presence of the defects leads to
resonant tunneling of the electromagnetic waves via local polariton modes
accompanied by resonant enhancement of the field inside the sample, even when a
realistic absorption is taken into account. On the basis of the results
obtained, we make recommendations regarding the experimental observation of the
effects studied in readily available samples.Comment: 17 pages, 10 figures, RevTex, Submitted to PR
Unifying discrete and continuous Weyl-Titchmarsh theory via a class of linear Hamiltonian systems on Sturmian time scales
In this study, we are concerned with introducing Weyl-Titchmarsh theory for a
class of dynamic linear Hamiltonian nabla systems over a half-line on Sturmian
time scales. After developing fundamental properties of solutions and regular
spectral problems, we introduce the corresponding maximal and minimal operators
for the system. Matrix disks are constructed and proved to be nested and
converge to a limiting set. Some precise relationships among the rank of the
matrix radius of the limiting set, the number of linearly independent square
summable solutions, and the defect indices of the minimal operator are
established. Using the above results, a classification of singular dynamic
linear Hamiltonian nabla systems is given in terms of the defect indices of the
minimal operator, and several equivalent conditions on the cases of limit point
and limit circle are obtained, respectively. These results unify and extend
certain classic and recent results on the subject in the continuous and
discrete cases, respectively, to Sturmian time scales.Comment: 34 page
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